Exact Differential Equations — Engineering Board Exam Practice Questions

14 free engineering board exam reviewer questions on Exact Differential Equations (Differential Equations), each with the correct answer and a worked solution.

1. Determine whether (2xy),dx+(x2+1),dy=0 is an exact differential equation.
2. Solve the exact differential equation (2xy),dx+(x2+1),dy=0.
3. Determine whether (3x2+2y),dx+(2x+3y2),dy=0 is exact.
4. Solve the exact differential equation (3x2+2y),dx+(2x+3y2),dy=0.
5. Determine whether (y x+2xey),dx+( x+x2ey),dy=0 is exact.
6. Find the value of k that makes (2xy+ky2),dx+(x2+2xy),dy=0 exact.
7. Solve (2x+y),dx+(x-2y),dy=0 with y(1)=2 and find y(2).
8. Find the value of k for which (3x2y+ky3),dx+(x3+9xy2),dy=0 is exact.
9. Solve ≤ft(1+yexy )dx+≤ft(2y+xexy )dy=0.
10. Solve (ex y+3x2),dx+(ex y+2y),dy=0.
11. Solve (y x+2xey),dx+( x+x2ey-1),dy=0.
12. Solve (2xy+3),dx+(x2-1),dy=0.
13. For M=2xy, which choice of N makes M,dx+N,dy=0 exact?
14. Solve (3x2y+2),dx+(x3+4y),dy=0.