What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)=37sin(x) ?

The solution for (d^2y)/(dx^2)-6(dy)/(dx)=37sin(x) is y=c_{1}e^{6x}+c_{2}-sin(x)+6cos(x)

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(d^2y)/(dx^2)-6(dy)/(dx)=37sin(x)

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} = 37 sin (x)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} = 37 sin (x)

Solve linear ODE:

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

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

y^{^{''}} - 7 y^{^{'}} + 10 y = e^{x}

y^{^{''}} + k y = g - 6 t, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 8 y^{^{'}} + 16 y = 8 sin (4 x)

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

y^{^{''}} + y^{^{'}} - 2 y = t e^{3 t}

What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)=37sin(x) ?
The solution for (d^2y)/(dx^2)-6(dy)/(dx)=37sin(x) is y=c_{1}e^{6x}+c_{2}-sin(x)+6cos(x)