i fell asleep when the professor went over how to solve exact equations :-/ i know it's really easy but despite reading the chapter over and over i still can't get it right. please show me where i'm going wrong / what to do next.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Determine whether the equation in problem 1 is exact. If it is exact, find the solution.

[tex](2x + 3) + (2y - 2)y' = 0[/tex]

2. Relevant equations

3. The attempt at a solution

[tex](2x + 3)dx + (2y - 2)dy = 0[/tex]

[tex]M_{y} = 0 = N_{x} = 0[/tex] <--- the equation is exact

[tex]\psi_{x} = 0[/tex] --> [tex]\psi = \int^x 0dx = x + h(y)[/tex]

[tex]\frac{d\psi}{dy} = h'(y) = 2y - 2[/tex] ---> [tex]h(y)= y^2 - 2y[/tex]

and then i get stuck. i'm not sure where to go from there. the answer to the problem is [tex]x^2 + 3x + y^2 - 2y = c[/tex], which is apparent to me if you turn the original equation into a separable one, but that's not possible with all exact equations.

thanks for your time everyone.

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# Differential Equations: exact equation

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