4. Exact Equations and Substitutions

Homogeneous Substitutions — Quiz

Test your understanding of homogeneous substitutions with 5 practice questions.

Practice Questions

Question 1

What substitution is typically used to solve a homogeneous differential equation written in the form $dy/dx=F(y/x)$?

Question 2

If $y=vx$, what is $dy/dx$ in terms of $v$ and $x$?

Question 3

Which right-hand side is homogeneous of degree $0$ and can be written only in terms of $y/x$?

Question 4

Rewrite the differential equation $dy/dx=(x+y)/x$ using the substitution $y=vx$.

Question 5

Find the general solution of $dy/dx=y/x$ for $x\neq 0$.