Internal problem ID [3750]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1035.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}-a x y y^{\prime }+2 a y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 43
dsolve(diff(y(x),x)^3-a*x*y(x)*diff(y(x),x)+2*a*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {a \,x^{3}}{27} \\ y \relax (x ) = 0 \\ y \relax (x ) = \frac {x^{2}}{4 c_{1}}-\frac {x}{2 a c_{1}^{2}}+\frac {1}{4 a^{2} c_{1}^{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 135.157 (sec). Leaf size: 13176
DSolve[(y'[x])^3 -a x y[x] y'[x]+2 a y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
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