Internal problem ID [3317]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 575.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y y^{\prime } x^{2}-x^{2} \left (1+2 x \right )+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 33
dsolve(2*x^2*y(x)*diff(y(x),x) = x^2*(1+2*x)-y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {{\mathrm e}^{\frac {1}{x}} c_{1}+x^{2}} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{\frac {1}{x}} c_{1}+x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.531 (sec). Leaf size: 43
DSolve[2 x^2 y[x] y'[x]==x^2(1+2 x)-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x^2+c_1 e^{\frac {1}{x}}} \\ y(x)\to \sqrt {x^2+c_1 e^{\frac {1}{x}}} \\ \end{align*}