Internal problem ID [6463]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve((1+x^2)*diff(y(x),x$2)+diff(y(x),x)^3=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \int \frac {1}{\sqrt {c_{1} +2 \arctan \left (x \right )}}d x +c_{2} \\ y \left (x \right ) = \int -\frac {1}{\sqrt {c_{1} +2 \arctan \left (x \right )}}d x +c_{2} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(1+x^2)*y''[x]+y[x]*(y'[x])^3==0,y[x],x,IncludeSingularSolutions -> True]
Not solved