Exercise
$y'=\frac{x^4+y^4}{xy^3}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation y^'=(x^4+y^4)/(xy^3). Rewrite the differential equation using Leibniz notation. We can identify that the differential equation \frac{dy}{dx}=\frac{x^4+y^4}{xy^3} is homogeneous, since it is written in the standard form \frac{dy}{dx}=\frac{M(x,y)}{N(x,y)}, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree. Use the substitution: y=ux. Expand and simplify.
Solve the differential equation y^'=(x^4+y^4)/(xy^3)
Final answer to the exercise
$y=\sqrt[4]{4\left(\ln\left(x\right)+c_0\right)}x,\:y=-\sqrt[4]{4\left(\ln\left(x\right)+c_0\right)}x$