Internal problem ID [7213]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+x {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve((1+x^2)*diff(y(x),x$2)+1+x*diff(y(x),x)^2=1,y(x), singsol=all)
\[ y \left (x \right ) = 2 \left (\int \frac {1}{\ln \left (x^{2}+1\right )+2 c_{1}}d x \right )+c_{2} \]
✓ Solution by Mathematica
Time used: 60.288 (sec). Leaf size: 33
DSolve[(1+x^2)*y''[x]+1+x*(y'[x])^2==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \int _1^x-\frac {2}{2 c_1-\log \left (K[1]^2+1\right )}dK[1]+c_2 \]