Solving: $\left(x+2y\right)dy-y\cdot dx=0$
Exercise
$\left(x+2y\right)dy-ydx$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation (x+2y)dy-ydx=0. We can identify that the differential equation \left(x+2y\right)dy-y\cdot dx=0 is homogeneous, 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 both are homogeneous functions of the same degree. Use the substitution: x=uy. Expand and simplify. Simplify the expression {0}.
Solve the differential equation (x+2y)dy-ydx=0
Final answer to the exercise
$\frac{x}{2y}=\ln\left|y\right|+C_0$