Internal problem ID [3449]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 711.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+y^{3} b \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.203 (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)
\[ y \relax (x ) = \frac {x \left (c_{1} x -a \RootOf \left (a^{2} \textit {\_Z}^{4}-2 a x c_{1} \textit {\_Z}^{3}+\left (a^{2} x^{2} c_{1}^{2}+b^{2} x^{2} c_{1}^{2}+x^{2} c_{1}^{2}-b^{2}\right ) \textit {\_Z}^{2}-2 a \,x^{3} c_{1}^{3} \textit {\_Z} +x^{4} c_{1}^{4}\right )\right )}{b \RootOf \left (a^{2} \textit {\_Z}^{4}-2 a x c_{1} \textit {\_Z}^{3}+\left (a^{2} x^{2} c_{1}^{2}+b^{2} x^{2} c_{1}^{2}+x^{2} c_{1}^{2}-b^{2}\right ) \textit {\_Z}^{2}-2 a \,x^{3} c_{1}^{3} \textit {\_Z} +x^{4} c_{1}^{4}\right )} \]
✓ Solution by Mathematica
Time used: 61.397 (sec). Leaf size: 13289
DSolve[(a x^3+(a x+b y[x])^3)y[x] y'[x]+x((a x+b y[x])^3+b y[x]^3)==0,y[x],x,IncludeSingularSolutions -> True]
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