29.33.31 problem 994

Internal problem ID [5570]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 994
Date solved : Monday, January 27, 2025 at 12:06:47 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 11.499 (sec). Leaf size: 93

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 \left (x \right ) &= \frac {x \left (-\operatorname {RootOf}\left (\textit {\_Z}^{16}+2 \textit {\_Z}^{4} c_{1} x^{4}-c_{1} x^{4}\right )^{4}+1\right )}{\operatorname {RootOf}\left (\textit {\_Z}^{16}+2 \textit {\_Z}^{4} c_{1} x^{4}-c_{1} x^{4}\right )^{4}} \\ y \left (x \right ) &= \frac {\frac {\operatorname {RootOf}\left (\textit {\_Z}^{16}-2 \textit {\_Z}^{4} c_{1} x^{4}-c_{1} x^{4}\right )^{12}}{c_{1}}-x^{4}}{x^{3}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 60.107 (sec). Leaf size: 3017

DSolve[(x^2-4 y[x]^2) (D[y[x],x])^2 +6 x y[x] D[y[x],x]-4 x^2+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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