Internal problem ID [3433]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 695.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x \left (x^{3}+3 y x^{2}+y^{3}\right ) y^{\prime }-\left (3 x^{2}+y^{2}\right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.074 (sec). Leaf size: 27
dsolve(x*(x^3+3*x^2*y(x)+y(x)^3)*diff(y(x),x) = (3*x^2+y(x)^2)*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left ({\mathrm e}^{3 \textit {\_Z}}+9 \,{\mathrm e}^{\textit {\_Z}}+3 c_{1}+3 \textit {\_Z} +3 \ln \relax (x )\right )} x \]
✓ Solution by Mathematica
Time used: 0.164 (sec). Leaf size: 37
DSolve[x(x^3+3 x^2 y[x]+y[x]^3)y'[x]==(3 x^2+y[x]^2)y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)^3}{3 x^3}+\frac {3 y(x)}{x}+\log \left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]