What is the solution for (d^2y)/(dx^2)-y=10sin^2(x) ?

The solution for (d^2y)/(dx^2)-y=10sin^2(x) is y=c_{1}e^x+c_{2}e^{-x}-10sin^2(x)-4cos(2x)

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(d^2y)/(dx^2)-y=10sin^2(x)

\frac{d ^{2} y}{d x ^{2}} - y = 10 sin^{2} (x)

y = c_{1} e^{x} + c_{2} e^{- x} - 10 sin^{2} (x) - 4 cos (2 x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} - y = 10 sin^{2} (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - 10 sin^{2} (x) - 4 cos (2 x)

y = c_{1} e^{x} + c_{2} e^{- x} - 10 sin^{2} (x) - 4 cos (2 x)

\frac{d}{d x} ((6 x^{3} + 6)^{3} (4 x)^{5 x})

\frac{d}{d x} (sin (x^{l n (x)}))

y = 4 9 - x^{2}

\frac{d}{d x} ((x^{2} - 1)^{- 1})

f (x) = 9 - 16 x

What is the solution for (d^2y)/(dx^2)-y=10sin^2(x) ?
The solution for (d^2y)/(dx^2)-y=10sin^2(x) is y=c_{1}e^x+c_{2}e^{-x}-10sin^2(x)-4cos(2x)