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H3. Solve the following differential equations d²y dy dr² dr dy dr 12 let y = exx => 1) 2) = +4 +4y=x²²e-²x₁ +9y=e³x (x²+7) =) ^² e^x +4xexx + 4exx = 0 =) So Ye= (A+Bx) e-³x So o yp=D² + 4D + 4 · X-² -.e-²x dry ax = ^e^x => 4x² = 1²e² →yp = ( D=21² +46D-2)+4 · *~².e-** 1 > D²-4x+4+40-8+4 x^2. e^?x D2.e-xx.2-2 : = e-zx. 0².x²2 =e-²x. SS x² dx dx =e-²x S-x+ dx = e-*x -[-\n(x)] -e-2x Inix) 2²+47 +4=0= ( 7+2, ² = 0 => ^)= -2 so y = y₁+ y₂ = (A+BX) e-2x - e-2x Inx. So y = (A+Bx) ex-e-2* lnx

H3. Solve the following differential equations d²y dy dr² dr dy dr 12 let y = exx => 1) 2) = +4 +4y=x²²e-²x₁ +9y=e³x (x²+7) =) ^² e^x +4xexx + 4exx = 0 =) So Ye= (A+Bx) e-³x So o yp=D² + 4D + 4 · X-² -.e-²x dry ax = ^e^x => 4x² = 1²e² →yp = ( D=21² +46D-2)+4 · *~².e-** 1 > D²-4x+4+40-8+4 x^2. e^?x D2.e-xx.2-2 : = e-zx. 0².x²2 =e-²x. SS x² dx dx =e-²x S-x+ dx = e-*x -[-\n(x)] -e-2x Inix) 2²+47 +4=0= ( 7+2, ² = 0 => ^)= -2 so y = y₁+ y₂ = (A+BX) e-2x - e-2x Inx. So y = (A+Bx) ex-e-2* lnx

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Could you explain why 'yp' can be solve by the way which showed in the picture, please

H3. Solve the following differential equations d²y dy dr² dr dy dr 12 let y = e** => exx 1) 2) +4 +4y=x²²e-²x₁ +9y=e³x (x²+7) =) ^² e^x +4xexx + 4exx = 0 =) > dry ax = ^e^x => 4x² = 1²e² So Ye= (A+Bx) e-³x So o yp=D² + 4D +4 · X-² -.e-²x = →yp = ( D=21² +46D-2)+4 · *~².e-** 1 D²-4x+4+40-8+4 x^2. e^?x Dz.e-xx. 7-2 = e-zx. 0².x²2 =e-²x. SS x² dx dx =e-²x S-x+ dx = e-*x -[-\n(x)] =-e-²x (nix) 2²+47 +4=0 = ( 7+2, ² = 0 => ^)= -2 so y = y₁+ y₂ = (A+BX) e-2x -e-2x Inx. So y = (A+Bx) e-x-e-2* lnx
Transcribed Image Text:H3. Solve the following differential equations d²y dy dr² dr dy dr 12 let y = e** => exx 1) 2) +4 +4y=x²²e-²x₁ +9y=e³x (x²+7) =) ^² e^x +4xexx + 4exx = 0 =) > dry ax = ^e^x => 4x² = 1²e² So Ye= (A+Bx) e-³x So o yp=D² + 4D +4 · X-² -.e-²x = →yp = ( D=21² +46D-2)+4 · *~².e-** 1 D²-4x+4+40-8+4 x^2. e^?x Dz.e-xx. 7-2 = e-zx. 0².x²2 =e-²x. SS x² dx dx =e-²x S-x+ dx = e-*x -[-\n(x)] =-e-²x (nix) 2²+47 +4=0 = ( 7+2, ² = 0 => ^)= -2 so y = y₁+ y₂ = (A+BX) e-2x -e-2x Inx. So y = (A+Bx) e-x-e-2* lnx
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