Internal problem ID [2085]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 2.406 (sec). Leaf size: 62
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)
\[ y \left (x \right ) = \frac {\sqrt {3}\, \sqrt {2}\, \sqrt {\frac {\left (54 x^{4}+6 \sqrt {3}\, \sqrt {27 x^{8}-2 x^{6}}\right )^{\frac {2}{3}}+6 x^{2}}{\left (54 x^{4}+6 \sqrt {3}\, \sqrt {27 x^{8}-2 x^{6}}\right )^{\frac {1}{3}}}}}{6} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{(y[x]^3+2*x^2*y[x])+(-3*x^3-2*x*y[x]^2)*y'[x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
Timed out