What is the solution for derivative of (dy/(dx))+1=0 ?

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

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derivative of (dy/(dx))+1=0

\frac{d}{d x} (\frac{d y}{d x}) + 1 = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 1 = 0

Isolate

y^{''} (x) : y^{''} (x) = - 1

Solve

y^{''} (x) = - 1 : y^{'} (x) = - x + c_{1}

Solve

y^{'} (x) = - x + c_{1} : y = - \frac{x ^{2}}{2} + c_{1} x + c_{2}

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

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