What is the solution for y^{''}+25y=20sin(5x) ?

The solution for y^{''}+25y=20sin(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)-2xcos(5x)

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y^{''}+25y=20sin(5x)

y^{^{''}} + 25 y = 20 sin (5 x)

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

Solution steps

y^{''} (x) + 25 y = 20 sin (5 x)

Solve linear ODE:

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

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

e^{x - y} d x + e^{y - x} d y = 0

y = 2 (x + 1), y = 3 (x + 1), x = 4

f (x^{2})

\frac{\partial}{\partial x} (\frac{1}{e ^{x}})

9 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0

What is the solution for y^{''}+25y=20sin(5x) ?
The solution for y^{''}+25y=20sin(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)-2xcos(5x)