Exercise
$\left(2xy^2+\frac{x}{y^2}\right)dx+4x^2ydy=0$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation (2xy^2+x/(y^2))dx+4x^2ydy=0. Group the terms of the equation. Grouping the terms of the differential equation. Combine all terms into a single fraction with y^2 as common denominator. Simplify \left(y^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2.
Solve the differential equation (2xy^2+x/(y^2))dx+4x^2ydy=0
Final answer to the exercise
$y=\frac{\sqrt[4]{C_2x^{-2}-1}}{\sqrt[4]{2}},\:y=\frac{-\sqrt[4]{C_2x^{-2}-1}}{\sqrt[4]{2}}$