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

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

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(d^2y)/(dx^2)=(dy)/(dx)+x

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 9 y = 6 \cdot sin (3 x) - 6 \cdot cos (- 3 x) + 36 \cdot e^{3 x}

y^{^{''}} - 49 y = 2 x e^{7 x}

(D^{2} + 4) y = x sin (x)

y^{^{''}} + 4 y + 4 y = 3, e^{- t} y (0) = 2

y^{^{''}} + 6 y^{^{'}} + 8 y = - 3 e^{- t}

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