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 see if it is possible to obtain an explicit form of the following differential equation

$$\left(\frac{dy}{dx}\right)^{2}=\frac{1}{ay^2+by+c}$$

where $a,b$ and $c\in\mathbb{R}$\{$0$}

share|improve this question
add comment

2 Answers 2

Hint: $$ \begin{align} x&=\int\sqrt{ay^2+by+c}\ \,\mathrm{d}y\\ &=\sqrt{a}\int\sqrt{\left(y-\frac{b}{2a}\right)^2-\frac{b^2-4ac}{4a^2}}\ \,\mathrm{d}y\\ \end{align} $$ A trig substitution often helps, but the particular substitution would depend on the sign of $b^2-4ac$.

share|improve this answer
add comment

HINT

Inverse your equation and get dx/dy. You now have to find x(y) and, may be, you could later inverse again to get y(x).

share|improve this answer
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.