What is the solution for y^{''}+7y^'=196sin(7t)+588cos(7t) ?

The solution for y^{''}+7y^'=196sin(7t)+588cos(7t) is y=c_{1}+c_{2}e^{-7t}+4sin(7t)-8cos(7t)

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y^{''}+7y^'=196sin(7t)+588cos(7t)

y^{^{''}} + 7 y^{^{'}} = 196 sin (7 t) + 588 cos (7 t)

y = c_{1} + c_{2} e^{- 7 t} + 4 sin (7 t) - 8 cos (7 t)

Solution steps

y^{''} (t) + 7 y^{'} (t) = 196 sin (7 t) + 588 cos (7 t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 7 t} + 4 sin (7 t) - 8 cos (7 t)

y = c_{1} + c_{2} e^{- 7 t} + 4 sin (7 t) - 8 cos (7 t)

x^{^{''}} + 49 x = 96 cos (5 t)

\frac{d ^{2} y}{d x ^{2}} - y = x e^{2 x}

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

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{2 x} + 1

What is the solution for y^{''}+7y^'=196sin(7t)+588cos(7t) ?
The solution for y^{''}+7y^'=196sin(7t)+588cos(7t) is y=c_{1}+c_{2}e^{-7t}+4sin(7t)-8cos(7t)