Internal problem ID [7217]
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: 0.016 (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 ) &= -\left (\int \frac {1}{\sqrt {c_{1} +2 \arctan \left (x \right )}}d x \right )+c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 62.161 (sec). Leaf size: 59
DSolve[(1+x^2)*y''[x]+y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \int _1^x-\frac {1}{\sqrt {2 \arctan (K[1])-2 c_1}}dK[1]+c_2 \\ y(x)\to \int _1^x\frac {1}{\sqrt {2 \arctan (K[2])-2 c_1}}dK[2]+c_2 \\ \end{align*}