15.18.34 problem 34

Internal problem ID [3277]
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
Date solved : Monday, January 27, 2025 at 07:30:27 AM
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*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.115 (sec). Leaf size: 20

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)
 

\[ y \left (x \right ) = -x +2 \ln \left (-x -1\right )+1-2 i \pi \]

✓ Solution by Mathematica

Time used: 7.253 (sec). Leaf size: 23

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

\[ y(x)\to -x+2 \log (-x-1)-2 i \pi +1 \]