Internal problem ID [88]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x y y^{\prime }-x^{2}-3 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(x*y(x)*diff(y(x),x) = x^2+3*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {4 x^{4} c_{1}-2}\, x}{2} \\ y \relax (x ) = \frac {\sqrt {4 x^{4} c_{1}-2}\, x}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.546 (sec). Leaf size: 42
DSolve[x*y[x]*y'[x] == x^2+3*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {-\frac {1}{2}+c_1 x^4} \\ y(x)\to x \sqrt {-\frac {1}{2}+c_1 x^4} \\ \end{align*}