Internal problem ID [2306]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}=-1} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 21
dsolve([(1+x^2)*diff(y(x),x$2)+1+diff(y(x),x)^2=0,y(0) = 1, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -x +2 \ln \left (-x -1\right )-2 i \pi +1 \]
✓ Solution by Mathematica
Time used: 6.806 (sec). Leaf size: 23
DSolve[{(1+x^2)*y''[x]+1+y'[x]^2==0,{y[0]==1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x+2 \log (-x-1)-2 i \pi +1 \]