Internal problem ID [7906]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 326.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y \left (\left (a y+x b \right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (a y+x b \right )^{3}+a y^{3}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.953 (sec). Leaf size: 160
dsolve(y(x)*((a*y(x)+b*x)^3+b*x^3)*diff(y(x),x)+x*((a*y(x)+b*x)^3+a*y(x)^3) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (c_{1} x -b \RootOf \left (b^{2} \textit {\_Z}^{4}-2 b x c_{1} \textit {\_Z}^{3}+\left (a^{2} x^{2} c_{1}^{2}+b^{2} x^{2} c_{1}^{2}+x^{2} c_{1}^{2}-a^{2}\right ) \textit {\_Z}^{2}-2 b \,x^{3} c_{1}^{3} \textit {\_Z} +x^{4} c_{1}^{4}\right )\right )}{a \RootOf \left (b^{2} \textit {\_Z}^{4}-2 b x c_{1} \textit {\_Z}^{3}+\left (a^{2} x^{2} c_{1}^{2}+b^{2} x^{2} c_{1}^{2}+x^{2} c_{1}^{2}-a^{2}\right ) \textit {\_Z}^{2}-2 b \,x^{3} c_{1}^{3} \textit {\_Z} +x^{4} c_{1}^{4}\right )} \]
✓ Solution by Mathematica
Time used: 62.278 (sec). Leaf size: 13289
DSolve[x*(a*y[x]^3 + (b*x + a*y[x])^3) + y[x]*(b*x^3 + (b*x + a*y[x])^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
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