What is the solution for y+2(d^2y)/(dx^2)=1 ?

The solution for y+2(d^2y)/(dx^2)=1 is y=c_{1}cos(x/(sqrt(2)))+c_{2}sin(x/(sqrt(2)))+1

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y+2(d^2y)/(dx^2)=1

y + 2 \frac{d ^{2} y}{d x ^{2}} = 1

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) + 1

Solution steps

y + 2 \frac{d ^{2} y}{d x ^{2}} = 1

Solve linear ODE:

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) + 1

y = c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2}) + 1

y^{^{''}} - 5 y = 3 sin (2 \cdot π \cdot x)

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

y^{^{''}} + y^{^{'}} = 7 sin (x)

y^{^{''}} + 2 y^{^{'}} - 1 = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{2} \cdot e^{(- 2 x)} + 1

What is the solution for y+2(d^2y)/(dx^2)=1 ?
The solution for y+2(d^2y)/(dx^2)=1 is y=c_{1}cos(x/(sqrt(2)))+c_{2}sin(x/(sqrt(2)))+1