What is the solution for ((x^3+1)/(x^2))(dy)/(dx)= 1/y ,y(0)=-1 ?

The solution for ((x^3+1)/(x^2))(dy)/(dx)= 1/y ,y(0)=-1 is y=-sqrt((2ln(x^3+1)+3)/3)

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((x^3+1)/(x^2))(dy)/(dx)= 1/y ,y(0)=-1

(\frac{x ^{3} + 1}{x ^{2}}) \frac{d y}{d x} = \frac{1}{y}, y (0) = - 1

y = - \frac{2 ln ( x ^{3} + 1 ) + 3}{3}

Solution steps

(\frac{x ^{3} + 1}{x ^{2}}) \frac{d y}{d x} = \frac{1}{y}

Solve separable ODE:

y = - \frac{2 ln ( x ^{3} + 1 ) + 3}{3}

y = - \frac{2 ln ( x ^{3} + 1 ) + 3}{3}

e^{x + y} \cdot \frac{d y}{d x} = x

x^{^{'}} = x^{7}

\frac{d v}{d t} = \frac{0.1}{v} \cdot \frac{0.25}{t}

y \frac{d y}{d x} = 3, x (y^{2} + 6)^{8} = 3

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

What is the solution for ((x^3+1)/(x^2))(dy)/(dx)= 1/y ,y(0)=-1 ?
The solution for ((x^3+1)/(x^2))(dy)/(dx)= 1/y ,y(0)=-1 is y=-sqrt((2ln(x^3+1)+3)/3)