83.46.6 problem Ex 6 page 71

Internal problem ID [19571]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter V. Singular solutions
Problem number : Ex 6 page 71
Date solved : Tuesday, January 28, 2025 at 01:57:18 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.070 (sec). Leaf size: 29

dsolve(diff(y(x),x)^3-4*x*y(x)*diff(y(x),x)+8*y(x)^2=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {4 x^{3}}{27} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (4 c_{1} x -1\right )^{2}}{64 c_{1}^{3}} \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],x]^3-4*x*y[x]*D[y[x],x]+8*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out