4. Exact Equations and Substitutions

Exact Equations — Quiz

Test your understanding of exact equations with 5 practice questions.

Practice Questions

Question 1

Which condition must hold for the differential equation $M(x,y)\,dx+N(x,y)\,dy=0$ to be exact on a suitable domain?

Question 2

Is the differential equation $(2xy+3)\,dx+(x^2+4y)\,dy=0$ exact?

Question 3

If $F(x,y)=x^2y+e^y$, what differential equation is given by $dF=0$?

Question 4

Find a potential function $F(x,y)$ for the exact differential equation $(2xy+3x)\,dx+(x^2+4y)\,dy=0$.

Question 5

A solution of the exact equation $2x\,dx+2y\,dy=0$ passes through $(1,2)$. What implicit equation describes that solution?