Final answer to the problem
Step-by-step Solution
Specify the solving method
Rewrite the differential equation
Learn how to solve differential equations problems step by step online.
$\frac{dy}{dx}=\frac{e^x}{y}$
Learn how to solve differential equations problems step by step online. Solve the differential equation (ydy)/dx=e^x. Rewrite the differential equation. Rewrite the differential equation in the standard form M(x,y)dx+N(x,y)dy=0. The differential equation ydy-e^xdx=0 is exact, since it is written in the standard form M(x,y)dx+N(x,y)dy=0, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and they satisfy the test for exactness: \displaystyle\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}. In other words, their second partial derivatives are equal. The general solution of the differential equation is of the form f(x,y)=C. Using the test for exactness, we check that the differential equation is exact.