What is the solution for y^{''}-6y^'=37sin(x) ?

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

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y^{''}-6y^'=37sin(x)

y^{^{''}} - 6 y^{^{'}} = 37 sin (x)

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

Solution steps

y^{''} (x) - 6 y^{'} (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^{^{''}} - 4 y^{^{'}} + 3 y = 3 e^{- 2 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + y = 20 sin (x)

y^{^{''}} + 4 y = cos (3 x)

2 y^{^{''}} - 16 y + 4 = 0

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = e^{x} + 1

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