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}

y^{^{''''}} - 5 y^{^{''}} + 4 y = 20 e^{3 x}

y^{^{''}} + 36 y = 12 tan (6 t)

(- 8 x^{^{''}} - 16 x^{^{'}} + 24) = 8 e^{2 t}

y^{^{''}} - y^{^{'}} + 2 y = 4 e^{x}

y^{^{''}} - 3 y^{^{'}} - 6 y = 2 e^{2 x} + 4

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