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
8th Edition
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea7bbfe4-f0d9-4343-839c-f9e5c129de8e%2Fe8fa2581-f636-4b73-881d-866a06fcc28a%2Fob9w4h_processed.jpeg&w=3840&q=75)
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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