What is the solution for y^{''}+25y=32sin(3x+2) ?

The solution for y^{''}+25y=32sin(3x+2) is y=c_{1}cos(5x)+c_{2}sin(5x)+2sin(3x+2)

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y^{''}+25y=32sin(3x+2)

y^{^{''}} + 25 y = 32 sin (3 x + 2)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + 2 sin (3 x + 2)

Solution steps

y^{''} (x) + 25 y = 32 sin (3 x + 2)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + 2 sin (3 x + 2)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + 2 sin (3 x + 2)

y^{^{'''}} - 15 y^{^{''}} + 500 y = e^{10 x}

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

x^{^{''}} - c^{2} x = c cos (c t + a)

x^{^{''}} - 3 x^{^{'}} + 2 x = \frac{( e ^{2 t} )}{e ^{2 t} + 1}

y^{^{'''}} - 9 y^{^{''}} + 27 y^{^{'}} - 27 y = 3 e^{3 x}

What is the solution for y^{''}+25y=32sin(3x+2) ?
The solution for y^{''}+25y=32sin(3x+2) is y=c_{1}cos(5x)+c_{2}sin(5x)+2sin(3x+2)