What is the solution for xy(dy)/(dx)=x^2+1 ?

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

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xy(dy)/(dx)=x^2+1

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

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

Solution steps

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

Solve separable ODE:

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

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

(y - 1) sin (x) d x - d y = 0

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

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

e^{y} y^{^{'}} - x^{2} = 0

y (169 - x^{2})^{\frac{1}{2}} d y = (169 + y^{2})^{\frac{1}{2}} d x

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