In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x. 1. y′′+16y=e3x 2. y′′−y′−2y=3x+4 3. y′′−y′−6y=2sin3x 4. 4y′′+4y′+y=3xex 5. y′′+y′+y=sin2x 6. 2y′′+4y′+7y=x2 7. y′′−4y=sinhx 8. y′′−4y=cosh2x 9. y′′+2y′−3y=1+xex 10. y′′+9y=2cos3x+3sin3x 11. y(3)+4y′=3x−1 12.

(19) y ^ 5 + 2y ^ 3 + 2y '' = 3x ^ 2 - 1 its characteristic equation is

Resuelto In Problems 1 through 20, find a particular solution

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Pregunta: In Problems 1 through 20, find a particular solution yp of the given equation. In all these problems, primes denote derivatives with respect to x. 1. y′′+16y=e3x 2. y′′−y′−2y=3x+4 3. y′′−y′−6y=2sin3x 4. 4y′′+4y′+y=3xex 5. y′′+y′+y=sin2x 6. 2y′′+4y′+7y=x2 7. y′′−4y=sinhx 8. y′′−4y=cosh2x 9. y′′+2y′−3y=1+xex 10. y′′+9y=2cos3x+3sin3x 11. y(3)+4y′=3x−1 12.
question 19 please
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Solución
Paso 1
$(19)$
$y^{5} + 2 y^{3} + 2 y^{″} = 3 x^{2} - 1$
its characteristic equation is
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Paso 2
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Texto de la transcripción de la imagen:

In Problems 1 through 20, find a particular solution

y_{p}

of the given equation. In all these problems, primes denote derivatives with respect to

x

. 1.

y^{''} + 16 y = e^{3 x}

y^{''} - y^{'} - 2 y = 3 x + 4

y^{''} - y^{'} - 6 y = 2 sin 3 x

4 y^{''} + 4 y^{'} + y = 3 x e^{x}

y^{''} + y^{'} + y = sin^{2} x

2 y^{''} + 4 y^{'} + 7 y = x^{2}

y^{''} - 4 y = sinh x

y^{''} - 4 y = cosh 2 x

y^{''} + 2 y^{'} - 3 y = 1 + x e^{x}

10.

y^{''} + 9 y = 2 cos 3 x + 3 sin 3 x

11.

y^{(3)} + 4 y^{'} = 3 x - 1

12.

y^{(3)} + y^{'} = 2 - sin x

13.

y^{''} + 2 y^{'} + 5 y = e^{x} sin x

14.

y^{(4)} - 2 y^{''} + y = x e^{x}

15.

y^{(5)} + 5 y^{(4)} - y = 17

16.

y^{''} + 9 y = 2 x^{2} e^{3 x} + 5

17.

y^{''} + y = sin x + x cos x

18.

y^{(4)} - 5 y^{''} + 4 y = e^{x} - x e^{2 x}

19.

y^{(5)} + 2 y^{(3)} + 2 y^{''} = 3 x^{2} - 1

20.

y^{(3)} - y = e^{x} + 7