29.35.4 problem 1035

Internal problem ID [5602]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1035
Date solved : Monday, January 27, 2025 at 12:13:15 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} {y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.091 (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: 106.852 (sec). Leaf size: 13193

DSolve[(D[y[x],x])^3 -a*x*y[x]*D[y[x],x]+2*a*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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