Internal problem ID [11322]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first.
Article 57. Dependent variable absent. Page 132
Problem number: Ex 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}=-1} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 29
dsolve((1+x^2)*diff(y(x),x$2)+1+diff(y(x),x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{c_{1}}-\frac {\left (-c_{1}^{2}-1\right ) \ln \left (x c_{1} -1\right )}{c_{1}^{2}}+c_{2} \]
✓ Solution by Mathematica
Time used: 12.052 (sec). Leaf size: 33
DSolve[(1+x^2)*y''[x]+1+(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x \cot (c_1)+\csc ^2(c_1) \log (-x \sin (c_1)-\cos (c_1))+c_2 \]