Exercise
$\left(xy+x\right)dx-\left(x^2y^2+y^2+x^2+1\right)dy=0$
Step-by-step Solution
Learn how to solve special products problems step by step online. Solve the differential equation (xy+x)dx-(x^2y^2+y^2x^2+1)dy=0. Factoring by x. Grouping the terms of the differential equation. Multiply both sides of the equation by -1. Factor the polynomial \cdot xdx+\cdot xydx by it's greatest common factor (GCF): \cdot xdx.
Solve the differential equation (xy+x)dx-(x^2y^2+y^2x^2+1)dy=0
Final answer to the exercise
$\frac{1}{2}y^2-y+2\ln\left|y+1\right|=\frac{1}{2}\ln\left|x^2+1\right|+C_0$