15.8.51 problem 54

Internal problem ID [3054]
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 : 54
Date solved : Monday, January 27, 2025 at 07:12:47 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

With initial conditions

\begin{align*} y \left (2\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 11.333 (sec). Leaf size: 255

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

\[ y = \frac {x^{2} \left (-\frac {\sqrt {10}\, {\left (\sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{2}/{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}}}}+\sqrt {\frac {4 \sqrt {10}\, x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}}-\sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{2}/{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}}}}\, \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{2}/{3}}-20 \sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{2}/{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}}}}}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}} \sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{2}/{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{{1}/{3}}}}}}\right )}^{3}}{20}+8\right )}{12} \]

✗ Solution by Mathematica

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

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

Timed out