Exercise
$y\ln\left(x\right)\frac{dy}{dx}=\frac{\left(y+1\right)^2}{x}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation yln(x)dy/dx=((y+1)^2)/x. 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 \frac{y}{\left(y+1\right)^2}dy. Simplify the expression \frac{1}{\ln\left(x\right)}\frac{1}{x}dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Solve the differential equation yln(x)dy/dx=((y+1)^2)/x
Final answer to the exercise
$\ln\left|y+1\right|+\frac{1}{y+1}=\ln\left|\ln\left|x\right|\right|+C_0$