What is the solution for y^{''}-5y^'+6y=sin(x) ?

The solution for y^{''}-5y^'+6y=sin(x) is y=c_{1}e^{3x}+c_{2}e^{2x}+1/10 sin(x)+1/10 cos(x)

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y^{''}-5y^'+6y=sin(x)

y^{^{''}} - 5 y^{^{'}} + 6 y = sin (x)

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{1}{10} sin (x) + \frac{1}{10} cos (x)

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = sin (x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{1}{10} sin (x) + \frac{1}{10} cos (x)

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{1}{10} sin (x) + \frac{1}{10} cos (x)

\int sec^{2} (3 θ) d θ

x \to 8 - lim (\frac{x}{ln ( 9 - x )})

\frac{d}{d x} (arctan (x - 1))

y^{^{'}} - (\frac{2 x}{( 1 + x ^{2} )}) y = 0

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What is the solution for y^{''}-5y^'+6y=sin(x) ?
The solution for y^{''}-5y^'+6y=sin(x) is y=c_{1}e^{3x}+c_{2}e^{2x}+1/10 sin(x)+1/10 cos(x)