Internal problem ID [4258]
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]]
\[ \boxed {{y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2}=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 33
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 \left (x \right ) &= \frac {a \,x^{3}}{27} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (a c_{1} x -1\right )^{2}}{4 c_{1}^{3} a^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 146.625 (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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