What is the solution for y^{''}+y^'=6sin(2x) ?

The solution for y^{''}+y^'=6sin(2x) is y=c_{1}+c_{2}e^{-x}-6/5 sin(2x)-3/5 cos(2x)

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y^{''}+y^'=6sin(2x)

y^{^{''}} + y^{^{'}} = 6 sin (2 x)

y = c_{1} + c_{2} e^{- x} - \frac{6}{5} sin (2 x) - \frac{3}{5} cos (2 x)

Solution steps

y^{''} (x) + y^{'} (x) = 6 sin (2 x)

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} - \frac{6}{5} sin (2 x) - \frac{3}{5} cos (2 x)

y = c_{1} + c_{2} e^{- x} - \frac{6}{5} sin (2 x) - \frac{3}{5} cos (2 x)

x \to 8 lim (\frac{5 x - 2}{x + 8})

\int_{- 2}^{2} x^{2} 4 - x^{2} d x

5 x + 3 x

s \to 1 lim (\frac{s ^{3} - 1}{s - 1})

x \to 6 lim (5 x)

What is the solution for y^{''}+y^'=6sin(2x) ?
The solution for y^{''}+y^'=6sin(2x) is y=c_{1}+c_{2}e^{-x}-6/5 sin(2x)-3/5 cos(2x)