Solve y'=y^2 - ScanMath

Evaluate

y^{'} = y^{2}

Rewrite the expression

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

Rewrite the expression

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

Multiply the terms

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

Transform the expression

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

Integrate the left-hand side of the equation with respect to y and the right-hand side of the equation with respect to x

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

Calculate

More Steps

- \frac{1}{y} + C_{1} = \int 1 d x, C_{1} \in R

Calculate

More Steps

- \frac{1}{y} + C_{1} = x + C_{2}, C_{1} \in R, C_{2} \in R

Since the integral constants C_{1} and C_{2} are arbitrary constants, replace them with constant C

- \frac{1}{y} = x + C, C \in R

Solution

More Steps

y = - \frac{1}{x + C}, C \in R

Solve the differential equation