15.8.53 problem 56

Internal problem ID [3056]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 56
Date solved : Monday, January 27, 2025 at 07:12:54 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 3.958 (sec). Leaf size: 73

dsolve([(y(x)^3+2*x^2*y(x))+(-3*x^3-2*x*y(x)^2)*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
 

\[ y = \frac {\sqrt {3}\, \sqrt {2}\, \sqrt {\frac {\left (54 x^{4}+6 \sqrt {3}\, \sqrt {27 x^{8}-2 x^{6}}\right )^{{2}/{3}}+6 x^{2}}{\left (54 x^{4}+6 \sqrt {3}\, \sqrt {27 x^{8}-2 x^{6}}\right )^{{1}/{3}}}}}{6} \]

✗ Solution by Mathematica

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

DSolve[{(y[x]^3+2*x^2*y[x])+(-3*x^3-2*x*y[x]^2)*D[y[x],x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

Timed out