What is the solution for (d^2y)/(dx^2)+a(dy)/(dx)=g ?

The solution for (d^2y)/(dx^2)+a(dy)/(dx)=g is y=c_{1}+c_{2}e^{-ax}+(gx)/a

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(d^2y)/(dx^2)+a(dy)/(dx)=g

\frac{d ^{2} y}{d x ^{2}} + a \frac{d y}{d x} = g

y = c_{1} + c_{2} e^{- a x} + \frac{gx}{a}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + a \frac{d y}{d x} = g

Solve linear ODE:

y = c_{1} + c_{2} e^{- a x} + \frac{gx}{a}

y = c_{1} + c_{2} e^{- a x} + \frac{gx}{a}

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

9 y^{^{''}} - 16 y = sin (x)

y^{^{'''}} + y^{^{'}} - 10 y = 29 e^{4 x}

f^{^{''}} (x) + 3 f^{^{'}} (x) + 2 f (x) = 2, f (0) = 3, f^{^{'}} (0) = 5

y^{^{''}} - 6 y^{^{'}} + 10 y = 180 sin (2 x)

What is the solution for (d^2y)/(dx^2)+a(dy)/(dx)=g ?
The solution for (d^2y)/(dx^2)+a(dy)/(dx)=g is y=c_{1}+c_{2}e^{-ax}+(gx)/a