Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm trying to solve the following differential equation:

$$ \frac{dy}{dx} = - \frac{3x + 2y}{2y}. $$

It looks pretty simple, yet it's not separable, linear, or exact. It is of the form

$$ \frac{dy}{dx} = f(y/x). $$

I could do the substitution $v = y/x$, and I know it would look pretty ugly, but is there a better or simpler method?

share|improve this question
    
Doubt it: wolframalpha.com/input/… –  user7530 Feb 23 '13 at 3:59
add comment

1 Answer

up vote 4 down vote accepted

One way I can think is to solve: $$ \frac{dy}{dt} = -3 x - 2y \\ \frac{dx}{dt} = 2 y $$ say by matrix exponentiation. Then one can invert $ x(t) $ to find $ y(x) $.

share|improve this answer
    
For the qualitative end behavior of the solution, I like the matrix solution. The associated matrix is $$\begin{pmatrix} 0 & 2 \\ -3 & -2 \end{pmatrix},$$ which leads to the eigenvalues $-1 \pm i\sqrt{5}$. So I can have overall sense of the family of solutions. In particular, I can tell that they must "go" through the origin. –  Minh Feb 23 '13 at 4:29
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.