What is the solution for y^{''}+200/8*y=30sin(2x),y(0)=2,y^'(0)=0 ?

The solution for y^{''}+200/8*y=30sin(2x),y(0)=2,y^'(0)=0 is y=2cos(5x)-4/7 sin(5x)+10/7 sin(2x)

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y^{''}+200/8*y=30sin(2x),y(0)=2,y^'(0)=0

y^{^{''}} + \frac{200}{8} \cdot y = 30 sin (2 x), y (0) = 2, y^{^{'}} (0) = 0

y = 2 cos (5 x) - \frac{4}{7} sin (5 x) + \frac{10}{7} sin (2 x)

Solution steps

y^{''} (x) + \frac{200}{8} \cdot y = 30 sin (2 x)

Solve linear ODE:

y = 2 cos (5 x) - \frac{4}{7} sin (5 x) + \frac{10}{7} sin (2 x)

y = 2 cos (5 x) - \frac{4}{7} sin (5 x) + \frac{10}{7} sin (2 x)

\frac{d}{d x} (- \frac{c}{x ^{2}})

\frac{2 x + 1}{x + 2}

3 t^{4} e^{- 2 t}

x^{5}, e^{3} x^{2}

\frac{2 s - 3}{s ^{2} + 4}

What is the solution for y^{''}+200/8*y=30sin(2x),y(0)=2,y^'(0)=0 ?
The solution for y^{''}+200/8*y=30sin(2x),y(0)=2,y^'(0)=0 is y=2cos(5x)-4/7 sin(5x)+10/7 sin(2x)