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Exact Equations Quizzes, Questions & Answers

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Exact Differential Equations: Identifying & Solving via ψ(x,y)

Exact Differential Equations: Identifying & Solving Via ψ(X,Y)

Ready to explore one of the most elegant ideas in differential equations? This quiz guides you through recognizing, verifying, and solving exact equations — where expressions behave like perfect derivatives of some...

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question 1
Which of the following differential equations is exact?

(2x + y)dx + (x + 2y)dy = 0

(x² + y)dx + (xy + 1)dy = 0

(3x² + 2xy)dx + (2x² + 3y)dy = 0

(y² + x)dx + (3xy + 1)dy = 0

Sample Question 2
For the exact equation (2x + y)dx + (x + 2y)dy = 0, what is the potential function ψ(x,y)?

ψ(x,y) = x² + xy + y²

ψ(x,y) = x² + 2xy + y²

ψ(x,y) = 2x² + xy + 2y²

ψ(x,y) = x² + xy + 2y²

Sample Question 3
The general solution to the exact equation (2x + y)dx + (x + 2y)dy = 0 is:

X² + xy + y² = C

2x² + xy + y² = C

X² + 2xy + y² = C

X² + xy + 2y² = C

Exact Equations Quizzes, Questions & Answers

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