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

The solution for (d^2y)/(dx^2)=ay+b is y=c_{1}e^{sqrt(a)x}+c_{2}e^{-sqrt(a)x}-b/a

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(d^2y)/(dx^2)=ay+b

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{'}} + 5 y = 10 cos (5 t)

y^{^{''}} - 4 y^{^{'}} - 12 y = sin (3 t)

\frac{d ^{2} y}{d x ^{2}} + 9 y = - 15 x + 7 + e^{x}

y^{^{''}} + 9 y = sin (3 x) + e^{2 x}

y^{^{''}} - y^{^{'}} - 2 y = 8 x + 5

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