Exercise
$2\:ydx+xdy=xy^3dy$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation 2ydx+xdy=xy^3dy. Group the terms of the equation. Factor the polynomial x\cdot dy-xy^3dy by it's greatest common factor (GCF): x\cdot dy. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression \left(1-y^{3}\right)\frac{1}{y}dy.
Solve the differential equation 2ydx+xdy=xy^3dy
Final answer to the exercise
$\ln\left|y\right|+\frac{-y^{3}}{3}=-2\ln\left|x\right|+C_0$