Step-by-step explanation
Problem to solve:
$\frac{dy}{dx}=\frac{x}{y}$
Learn how to solve differential equations problems step by step online.
$y\cdot dy=x\cdot dx$
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=x/y. 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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int ydy and replace the result in the differential equation. Solve the integral \int xdx and replace the result in the differential equation.
Final Answer
$y=\sqrt{2\left(\frac{1}{2}x^2+C_0\right)},\:y=-\sqrt{2\left(\frac{1}{2}x^2+C_0\right)}$