29.25.14 problem 711

Internal problem ID [5301]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 711
Date solved : Monday, January 27, 2025 at 11:05:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+b y^{3}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.937 (sec). Leaf size: 160

dsolve((a*x^3+(a*x+b*y(x))^3)*y(x)*diff(y(x),x)+x*((a*x+b*y(x))^3+b*y(x)^3) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x \left (c_{1} x -a \operatorname {RootOf}\left (a^{2} \textit {\_Z}^{4}-2 a x c_{1} \textit {\_Z}^{3}+\left (a^{2} c_{1}^{2} x^{2}+b^{2} c_{1}^{2} x^{2}+c_{1}^{2} x^{2}-b^{2}\right ) \textit {\_Z}^{2}-2 a \,x^{3} c_{1}^{3} \textit {\_Z} +c_{1}^{4} x^{4}\right )\right )}{b \operatorname {RootOf}\left (a^{2} \textit {\_Z}^{4}-2 a x c_{1} \textit {\_Z}^{3}+\left (a^{2} c_{1}^{2} x^{2}+b^{2} c_{1}^{2} x^{2}+c_{1}^{2} x^{2}-b^{2}\right ) \textit {\_Z}^{2}-2 a \,x^{3} c_{1}^{3} \textit {\_Z} +c_{1}^{4} x^{4}\right )} \]

✓ Solution by Mathematica

Time used: 61.819 (sec). Leaf size: 13289

DSolve[(a*x^3+(a*x+b*y[x])^3)*y[x]*D[y[x],x]+x*((a*x+b*y[x])^3+b*y[x]^3)==0,y[x],x,IncludeSingularSolutions -> True]
 

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