Exercise
$\frac{x+2}{y+1}\frac{dy}{dx}=\frac{x}{y}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation ((x+2)/(y+1)dy)/dx=x/y. Rewrite the differential equation. Divide fractions with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Divide fractions \frac{x}{\frac{\left(x+2\right)y}{y+1}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. 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.
Solve the differential equation ((x+2)/(y+1)dy)/dx=x/y
Final answer to the exercise
$y-\ln\left(y+1\right)=x-2\ln\left(x+2\right)+C_1-1$