What is the solution for y^{''}+10000y=100sin(50x) ?

The solution for y^{''}+10000y=100sin(50x) is y=c_{1}cos(100x)+c_{2}sin(100x)+1/75 sin(50x)

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y^{''}+10000y=100sin(50x)

y^{^{''}} + 10000 y = 100 sin (50 x)

y = c_{1} cos (100 x) + c_{2} sin (100 x) + \frac{1}{75} sin (50 x)

Solution steps

y^{''} (x) + 10000 y = 100 sin (50 x)

Solve linear ODE:

y = c_{1} cos (100 x) + c_{2} sin (100 x) + \frac{1}{75} sin (50 x)

y = c_{1} cos (100 x) + c_{2} sin (100 x) + \frac{1}{75} sin (50 x)

y^{^{''}} + 10 y^{^{'}} + 15 = 0

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} + x = 1

y^{^{''}} + y^{^{'}} - y = t \cdot e^{t}

x^{^{''}} + 12 x^{^{'}} + 11 x = 9 cos (2 t)

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

What is the solution for y^{''}+10000y=100sin(50x) ?
The solution for y^{''}+10000y=100sin(50x) is y=c_{1}cos(100x)+c_{2}sin(100x)+1/75 sin(50x)