What is the solution for (d^2y)/(dx^2)-(dy)/(dx)+5=0 ?

The solution for (d^2y)/(dx^2)-(dy)/(dx)+5=0 is y=c_{1}e^x+c_{2}+5x

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(d^2y)/(dx^2)-(dy)/(dx)+5=0

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + 5 = 0

y = c_{1} e^{x} + c_{2} + 5 x

Solution steps

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + 5 = 0

Solve linear ODE:

y = c_{1} e^{x} + c_{2} + 5 x

y = c_{1} e^{x} + c_{2} + 5 x

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

y^{^{''}} + 2 y^{^{'}} + 2 y = 6

y^{^{'''}} - 3 y^{^{''}} + 2 y^{^{'}} = x^{2} + 4 x + 8

y^{^{''}} - 8 y^{^{'}} + 16 y = 16 x + 8

y^{^{''}} - 2 y^{^{'}} + y = 4 x^{2} - 6 + x - 1 e x

What is the solution for (d^2y)/(dx^2)-(dy)/(dx)+5=0 ?
The solution for (d^2y)/(dx^2)-(dy)/(dx)+5=0 is y=c_{1}e^x+c_{2}+5x