What is the solution for (dy}{dx}=\frac{1+x)/y ?

The solution for (dy}{dx}=\frac{1+x)/y is y=sqrt(2x+x^2+c_{1)},y=-sqrt(2x+x^2+c_{1)}

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(dy}{dx}=\frac{1+x)/y

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

y = 2 x + x^{2} + c_{1}, y = - 2 x + x^{2} + c_{1}

Solution steps

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

Solve separable ODE:

y = 2 x + x^{2} + c_{1}, y = - 2 x + x^{2} + c_{1}

y = 2 x + x^{2} + c_{1}, y = - 2 x + x^{2} + c_{1}

y^{^{'}} = \frac{sin ( x )}{y}, y (\frac{π}{2}) = 1

(1 - cos (x)) (\frac{d y}{d x}) = y sin (x)

y^{^{'}} (x) = \frac{4 + 3 x ^{2}}{3 y ^{2} - 12 y}, y (0) = 2

(y cos (x)) d x + (3 sin (x)) d y = 0

y^{5} \frac{d y}{d x} = 2 x^{4} y^{6} - 4 x^{4}

What is the solution for (dy}{dx}=\frac{1+x)/y ?
The solution for (dy}{dx}=\frac{1+x)/y is y=sqrt(2x+x^2+c_{1)},y=-sqrt(2x+x^2+c_{1)}