81.2.5 problem 5

Internal problem ID [18613]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter II. Change of variable. Exercises at page 20
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 12:04:12 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved