What is the solution for y^{''}+25y=7x ?

The solution for y^{''}+25y=7x is y=c_{1}cos(5x)+c_{2}sin(5x)+(7x)/(25)

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y^{''}+25y=7x

y^{^{''}} + 25 y = 7 x

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{7 x}{25}

Solution steps

y^{''} (x) + 25 y = 7 x

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{7 x}{25}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{7 x}{25}

y^{^{''}} + y^{^{'}} - 6 y = 20 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

2 y^{^{''}} + 6 y^{^{'}} = 10 sin (7 t)

y^{^{''}} + 4 y = 16 t^{3} sin (2 t)

y^{^{''}} + 11 y^{^{'}} + 18 y = 5

y^{^{''}} - y^{^{'}} + 14 y = 2 + e^{\frac{x}{2}}

What is the solution for y^{''}+25y=7x ?
The solution for y^{''}+25y=7x is y=c_{1}cos(5x)+c_{2}sin(5x)+(7x)/(25)