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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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