What is the solution for y^{''}+25y=10cos(5x) ?

The solution for y^{''}+25y=10cos(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+xsin(5x)

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y^{''}+25y=10cos(5x)

y^{^{''}} + 25 y = 10 cos (5 x)

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

Solution steps

y^{''} (x) + 25 y = 10 cos (5 x)

Solve linear ODE:

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

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

y^{^{''}} + 0.01 (20 - y) = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 x + 7

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

\frac{1}{2} y^{^{''}} + \frac{1}{2} y^{^{'}} + 6 y = 10 cos (3 x)

y^{^{''}} + \frac{750}{30} y = \frac{20}{30} cos (2) t

What is the solution for y^{''}+25y=10cos(5x) ?
The solution for y^{''}+25y=10cos(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+xsin(5x)