Internal problem ID [997]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y y^{\prime } x -x^{2}-2 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(x*y(x)*diff(y(x),x)=x^2+2*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {x^{2} c_{1}-1}\, x \\ y \relax (x ) = -\sqrt {x^{2} c_{1}-1}\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.412 (sec). Leaf size: 38
DSolve[x*y[x]*y'[x]==x^2+2*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {-1+c_1 x^2} \\ y(x)\to x \sqrt {-1+c_1 x^2} \\ \end{align*}