Exercise
$6x-y\cdot\frac{dy}{dx}=x^2\:\cdot y\cdot\frac{dy}{dx}-3xy^2$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation 6x-ydy/dx=x^2ydy/dx-3xy^2. Group the terms of the equation. Factor the polynomial -y\left(\frac{dy}{dx}\right)-x^2y\left(\frac{dy}{dx}\right) by it's greatest common factor (GCF): -y\left(\frac{dy}{dx}\right). Rewrite the differential equation. Factoring by x.
Solve the differential equation 6x-ydy/dx=x^2ydy/dx-3xy^2
Final answer to the exercise
$\frac{1}{3}\ln\left|\frac{\sqrt{2}}{\sqrt{y^2+2}}\right|=-\frac{1}{2}\ln\left|1+x^2\right|+C_0$