Step-by-step Solution

Solve the differential equation $\frac{dx}{dy}=y+xy$

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Step-by-step explanation

Problem to solve:

$\frac{dx}{dy}=y+xy$

Learn how to solve differential equations problems step by step online.

$\frac{dx}{dy}=y\left(1+x\right)$

Unlock this full step-by-step solution!

Learn how to solve differential equations problems step by step online. Solve the differential equation dx/dy=y+xy. Factoring by y. Group the terms of the differential equation. Move the terms of the x variable to the left side, and the terms of the y variable to the right side. Integrate both sides, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{1+x}dx and replace the result in the differential equation.

Final Answer

$x=C_0e^{\frac{1}{2}y^2}-1$

Problem Analysis