56.3.21 problem 21

Internal problem ID [8879]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 21
Date solved : Monday, January 27, 2025 at 05:11:37 PM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 33

dsolve((1+x^2)*diff(y(x),x$2)+1+diff(y(x),x)^2=0,y(x), singsol=all)
 

\[ y = \frac {\ln \left (c_{1} x -1\right ) c_{1}^{2}+c_{2} c_{1}^{2}+c_{1} x +\ln \left (c_{1} x -1\right )}{c_{1}^{2}} \]

✓ Solution by Mathematica

Time used: 7.826 (sec). Leaf size: 33

DSolve[(1+x^2)*D[y[x],{x,2}]+1+(D[y[x],x])^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x \cot (c_1)+\csc ^2(c_1) \log (-x \sin (c_1)-\cos (c_1))+c_2 \]