Internal problem ID [2083]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{2}+\left (x^{3}-2 y x \right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 4.031 (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)
\[ y \left (x \right ) = \frac {x^{2} \left (-\frac {\sqrt {10}\, {\left (\sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{\frac {2}{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{\frac {1}{3}}}}+\sqrt {\frac {4 \sqrt {10}\, x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{\frac {1}{3}}-\sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{\frac {2}{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{\frac {1}{3}}}}\, \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{\frac {2}{3}}-20 \sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{\frac {2}{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{\frac {1}{3}}}}}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{\frac {1}{3}} \sqrt {\frac {\left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{\frac {2}{3}}+20}{x \left (20 x^{3}+20 \sqrt {x^{6}-20}\right )^{\frac {1}{3}}}}}}\right )}^{3}}{20}+8\right )}{12} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y[x]^2+(x^3-2*x*y[x])*y'[x]==0,{y[2]==1}},y[x],x,IncludeSingularSolutions -> True]
Timed out