Bt Bt

Find the general solution of the ordinary differential equation?

y'' - (b^2)y=e^(bt)

Where b is a non negative constant. Consider the cases; b=0 and b>0 separately.

Case 1: b = 0.
The DE reduces to y'' = 1.

Integrate both sides:
y = x + C₁

Integrate both sides again:
y = (1/2)x^2 + C₁ x + C₂.
-------------------------------
Case 2: b > 0.

Homogeneous solution:
The characteristic equation r^2 - b^2 = 0 has roots r = -b, b.
So, y_h = C₁ e^(bt) + C₂ e^(-bt).
----
Particular integral:
Due to the homogeneous solution, assume that y_p = Ate^(bt).

Differentiating yields
y' = Ae^(bt) + bAte^(bt) = Ae^(bt) (bt + 1).
y'' = bAe^(bt) (bt + 1) + Ae^(bt) * b = Ae^(bt) (b^2 t + 2b).

Substitute this into the DE:
Ae^(bt) (b^2 t + 2b) - b^2 * Ate^(bt) = e^(bt)
==> (2b) A = 1
==> A = 1/(2b).

So, the general solution is
y = C₁ e^(bt) + C₂ e^(-bt) + (1/(2b)) te^(bt).

I hope this helps!

Find Bt Bt On eBay Below:

BC 30D DUAL Charger For Topcon BT 62Q BT 65Q BT 66Q Battery
BC 30D DUAL Charger For Topcon BT 62Q BT 65Q BT 66Q Battery
$53.89
TOPCON BT 61Q BT 65Q Battery for Topcon GTS 720 GTS 750 GPT 7500 Total Station
TOPCON BT 61Q BT 65Q Battery for Topcon GTS 720 GTS 750 GPT 7500 Total Station
$42.00
NEW TOPCON BC 30D DUAL CHARGER FOR TOPCON BT 62Q BT 65Q BT 66Q BATTERIES
NEW TOPCON BC 30D DUAL CHARGER FOR TOPCON BT 62Q BT 65Q BT 66Q BATTERIES
$35.00
NEW TOPCON BT 52QA  3 PIN  72v Battery for TOPCON Instrument total stations
NEW TOPCON BT 52QA 3 PIN 72v Battery for TOPCON Instrument total stations
$36.00
New SOKKIA Single Charger for BDC70 BDC58 BDC46B BDC46 BDC46A BT L2 battery
New SOKKIA Single Charger for BDC70 BDC58 BDC46B BDC46 BDC46A BT L2 battery
$23.92
NEW TOPCON BC 30 SINGLE CHARGER FOR TOPCON BT 61Q BT 62Q BT 65Q BT 66Q BATTERIES
NEW TOPCON BC 30 SINGLE CHARGER FOR TOPCON BT 61Q BT 62Q BT 65Q BT 66Q BATTERIES
$23.00
Ni MH Battery Pack GTS GPT CTS Total Stations Topcon 51730 BT52Q
Ni MH Battery Pack GTS GPT CTS Total Stations Topcon 51730 BT52Q
$65.00
AdirPro Li Ion Battery for Topcon GTS 900 and GPT 9000 Total Station 77BT65Q
AdirPro Li Ion Battery for Topcon GTS 900 and GPT 9000 Total Station 77BT65Q
$97.95
Topcon BT 31Q Battery for Topcon Digital theodolite Total Stations
Topcon BT 31Q Battery for Topcon Digital theodolite Total Stations
$99.99
Coiled Cable Cygnus KS 102 Topcon Sokkia Trimble Specrea Surveying GPS GIS
Coiled Cable Cygnus KS 102 Topcon Sokkia Trimble Specrea Surveying GPS GIS
$49.99
New ORIGINAL Topcon BT 52Q Total Station Battery Pack Surveying BT 52QABT52Q
New ORIGINAL Topcon BT 52Q Total Station Battery Pack Surveying BT 52QABT52Q
$217.00
77BT30Q Battery TOPCON BT30Q Battery charges with the BC20CR charger
77BT30Q Battery TOPCON BT30Q Battery charges with the BC20CR charger
$299.99
NEW TOPCON BC 19B charger for topcon BT 32Q battery US standard outlet charger
NEW TOPCON BC 19B charger for topcon BT 32Q battery US standard outlet charger
$45.00
Replacement Battery Charger of Topcon BC 27CR Charges BT 50Q BT 52QA
Replacement Battery Charger of Topcon BC 27CR Charges BT 50Q BT 52QA
$39.71
Replacement Battery Charger of Topcon BC 30D Charges BT 65Q 66Q 61Q 60Q
Replacement Battery Charger of Topcon BC 30D Charges BT 65Q 66Q 61Q 60Q
$39.71
Replacement Battery of Topcon BT 32Q for GTS 220 210 200 series Totalstation
Replacement Battery of Topcon BT 32Q for GTS 220 210 200 series Totalstation
$35.29
Replacement Battery of Topcon BT 50Q for GTS 600 series Totalstation
Replacement Battery of Topcon BT 50Q for GTS 600 series Totalstation
$66.18
Replacement Battery of Topcon BT 65Q for GTS 720 750 900 series Totalstation
Replacement Battery of Topcon BT 65Q for GTS 720 750 900 series Totalstation
$39.71
NEW 10PCS TOPCON BATTERY BT 52QA  TOPCON Charger BC 27CR FOR TOTAL STATION
NEW 10PCS TOPCON BATTERY BT 52QA TOPCON Charger BC 27CR FOR TOTAL STATION
$830.00
Topcon BT 31QB Survey Instrument battery
Topcon BT 31QB Survey Instrument battery
$50.00
BT 52Q BATTERY FOR TOPCON TOTAL STATION SURVEYING BT 52QABT52QGPTGTS
BT 52Q BATTERY FOR TOPCON TOTAL STATION SURVEYING BT 52QABT52QGPTGTS
$79.00
Brand New BC 19B charger for TOPCON BT 32Q Battery total station
Brand New BC 19B charger for TOPCON BT 32Q Battery total station
$45.00
BC 20CR charger for TOPCON Battery BT 24Q and BT 30Q 2 PIN  TOTAL STATION
BC 20CR charger for TOPCON Battery BT 24Q and BT 30Q 2 PIN TOTAL STATION
$38.00
TOPCON BT 65Q BT65Q Li ion Battery for Topcon GTS 750 GPT 7500 Total Station
TOPCON BT 65Q BT65Q Li ion Battery for Topcon GTS 750 GPT 7500 Total Station
$35.00
Topcon MC I3 ASSYMC I3 FH915BTDUAL GPS
Topcon MC I3 ASSYMC I3 FH915BTDUAL GPS
$14,100.00
Trimble Bluetooth RGR BT0001 adapter for TSCe data collector
Trimble Bluetooth RGR BT0001 adapter for TSCe data collector
$142.99
BC L1 Li ion battery charger for GOWIN Battery BT L1 BT L1W total station
BC L1 Li ion battery charger for GOWIN Battery BT L1 BT L1W total station
$38.00
NEW Topcon BT 50Q Ni MH BATTERY BT50Q FOR TOPCON GTS602 GTS605 TOTAL STATIONS
NEW Topcon BT 50Q Ni MH BATTERY BT50Q FOR TOPCON GTS602 GTS605 TOTAL STATIONS
$65.00
BT 65Q Li Ion Battery for Topcon GTS 900 and GPT 9000 Total Station
BT 65Q Li Ion Battery for Topcon GTS 900 and GPT 9000 Total Station
$122.41
BDC 58 BT LT2 BATTERY FOR SOKKIATOPCON TOTAL STATIONGPSSRXGRXROBOTICGR
BDC 58 BT LT2 BATTERY FOR SOKKIATOPCON TOTAL STATIONGPSSRXGRXROBOTICGR
$89.00
Topcon ITS 1 Survey Total Station with Case and Extra Battery BT 20Q and Parts
Topcon ITS 1 Survey Total Station with Case and Extra Battery BT 20Q and Parts
$695.00
Leica TS12 P R400 Reflectorless Long Range BT Robotic Total Station 5 Sec 1205
Leica TS12 P R400 Reflectorless Long Range BT Robotic Total Station 5 Sec 1205
$16,499.99


Recently Purchased Bt Bt:


leica geb212 replacement battery for gps1200 gps900 grx1200 series, st cardport assy with btwifi no sdio tsc2 rohs, new topcon bc20cr charger for topcon bt24q bt30q battery 2pin charger, new topcon bc27cr charger for topcon bt52q bt 52qa battery, trimble tsc2 data collector 24ghz internal radio bt wifi access 201612, trimble tsc2 data collector 24ghz radio bt wifi survey controller 1250 , new trimble tds nomad 800g series 6gb gps wifi bt bluetooth rugged handheld pda, battery for total station topcon bt35q surveyor 49, topcon bt19q battery w replaceable fuse, topcon onboard battery bt34q, topcon btg1w total station onboard battery, topcon bt52qa battery assembly housing shield case no cells, topcon its1 survey total station with case and extra battery bt20q , topcon bc30d charger amp; bt66q liion 74v 2410mah battery survey instrument, topcon 51743 heavy duty charger bc6 for bt3l 3pin, topcon bt52qa 3 pin battery for topcon instrument total stations, topcon bt15q battery for total station fdk sanyo new cell, new topcon bt61q 74v battery for topcon gts720gts750gpt7500 total station, 2 topcon bt20q handle battery topcon total stations gts4 asis untested, topcon bt5q battery for topcon total station gts2b, new topcon bt61q battery 74v 4400mah for topcon total stations, bt l1a liion battery for gowin total station , new topcon btl2 battery for topcon esos and sokkia total station, new topcon bt32q nicd battery for topcon total stations free shipping, bt l1 w liion battery for gowin total station 74v liion 3000mah, new topcon bt65q battery bc30 charger for topcon bt65q bt65q battery, topcon its1 survey total station with case and extra battery bt20q and parts, topcon mci3 assymci3 fh915btdual gps, new 10pcs topcon battery bt52qa amp; topcon charger bc27cr for total station, new topcon bc20cr charger for topcon bt24q bt30q 2 pin charger, bt 65q liion battery for topcon gts 900 and gpt 9000 total station, new topcon bt50q nimh battery bt50q for topcon gts602 gts605 total stations, topcon bt52qa 3 pin 2700mah battery for topcon instrument total stations, topcon 56134 rlh series laser charger for bt25q battery, trimble juno sb dc wm6 wifi bt with tds survey pro 453 full activated, leica icon cc61 7 yellow tablet pc w long range bt batteries and charger, topcon bc19b charger for topcon bt32q battery total station, leica ts15 p r400 reflectorless long range bt robotic total station 3 sec 1203, brand new topcon bt66q battery for topcon total stations 74v 2500mah, topcon bc30 bc30d dual charger for batteries bt62q bt65q bt66q, bcl1 li ion battery charger for gowin battery btl1 btl1w total station, new 3pin topcon equivalent charger for topcon bt52q bt50q tbb2 batterie, new topcon bc19bcr charger for topcon battery bt32q charger total station, topcon bc27cr charger for topcon toptal station bt52q bt52qa battery 3 pin, topcon bt52qa total station battery for topcon gtsgpt series surveying bt52q, 5pcs topcon bt66q battery for topcon gpt7500 gpt9000 total stations, brand new topcon bc30 bt62q bt66q liion for topcon 74v 2500mah, topcon bt52q nimh battery with bc27cr charger for topcon total station, new gowin btl1 battery for gowin 202 tks202 tks202r total stations surveying, topcon btl2 72 4300mah liion battery for topcon esos sokkia total stations , new topcon bt65q battery for topcon gts750gpt7500 total stations, new battery for south 9600 s82 btl72s ruide gps rtk gnss 2300mah survey battery, trimble tds ranger data collector battery for tsce ranger 200 bttrmbtsce, topcon survey bt47q amp; bt56q new battery insert 72v38ah, topcon survey bt24q amp; bt30q new battery insert 72v30ah, topcon survey bt15q amp; bt20q new battery insert 84v30ah, compatible battery for topcon bt56q charger survey instrument



Comments are closed.