What is the solution for y^{''}+25y=x+sin(x) ?

The solution for y^{''}+25y=x+sin(x) is y=c_{1}cos(5x)+c_{2}sin(5x)+x/(25)+1/24 sin(x)

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y^{''}+25y=x+sin(x)

y^{^{''}} + 25 y = x + sin (x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x}{25} + \frac{1}{24} sin (x)

Solution steps

y^{''} (x) + 25 y = x + sin (x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x}{25} + \frac{1}{24} sin (x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x}{25} + \frac{1}{24} sin (x)

y^{^{''}} - 4 y = 8 e^{3 x}

x^{^{''}} + 25 x = 32 cos (3 t)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 6

2 y^{^{''}} + y^{^{'}} + 3 y = 3 cos (3 t) + 2 sin (3 t)

y^{^{''}} - y = x^{2}, y (0) = - 3, y^{^{'}} (0) = 5

What is the solution for y^{''}+25y=x+sin(x) ?
The solution for y^{''}+25y=x+sin(x) is y=c_{1}cos(5x)+c_{2}sin(5x)+x/(25)+1/24 sin(x)