Internal problem ID [90]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x y y^{\prime }-y^{2}-x \sqrt {4 x^{2}+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 26
dsolve(x*y(x)*diff(y(x),x) = y(x)^2+x*(4*x^2+y(x)^2)^(1/2),y(x), singsol=all)
\[ -\frac {\sqrt {4 x^{2}+y \relax (x )^{2}}}{x}+\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.273 (sec). Leaf size: 48
DSolve[x*y[x]*y'[x] == y[x]^2+x*(4*x^2+y[x]^2)^(1/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {(\log (x)-2+c_1) (\log (x)+2+c_1)} \\ y(x)\to x \sqrt {(\log (x)-2+c_1) (\log (x)+2+c_1)} \\ \end{align*}