- #1
jimmypoopins
- 65
- 0
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.
Determine whether the equation in problem 1 is exact. If it is exact, find the solution.
[tex](2x + 3) + (2y - 2)y' = 0[/tex]
[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.
Homework Statement
Determine whether the equation in problem 1 is exact. If it is exact, find the solution.
[tex](2x + 3) + (2y - 2)y' = 0[/tex]
Homework Equations
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.