Internal problem ID [3718]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 994.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (x^{2}-4 y^{2}\right ) \left (y^{\prime }\right )^{2}+6 y y^{\prime } x -4 x^{2}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 2.453 (sec). Leaf size: 92
dsolve((x^2-4*y(x)^2)*diff(y(x),x)^2+6*x*y(x)*diff(y(x),x)-4*x^2+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x \left (\RootOf \left (\textit {\_Z}^{16}+2 \textit {\_Z}^{4} x^{4} c_{1}-x^{4} c_{1}\right )^{4}-1\right )}{\RootOf \left (\textit {\_Z}^{16}+2 \textit {\_Z}^{4} x^{4} c_{1}-x^{4} c_{1}\right )^{4}} \\ y \relax (x ) = \frac {\frac {\RootOf \left (\textit {\_Z}^{16}-2 \textit {\_Z}^{4} x^{4} c_{1}-x^{4} c_{1}\right )^{12}}{c_{1}}-x^{4}}{x^{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.103 (sec). Leaf size: 3017
DSolve[(x^2-4 y[x]^2) (y'[x])^2 +6 x y[x] y'[x]-4 x^2+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
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