Internal problem ID [4166]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 8. Special second order equations. Lesson 35. Independent variable x
absent
Problem number: Exercise 35.23(c), page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {x y y^{\prime \prime }-2 x \left (y^{\prime }\right )^{2}+\left (1+y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 22
dsolve(x*y(x)*diff(y(x),x$2)-2*x*(diff(y(x),x))^2+(1+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = c_{1} \tanh \left (\frac {\ln \relax (x )-c_{2}}{2 c_{1}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 37
DSolve[x*y[x]*y''[x]-2*x*(y'[x])^2+(1+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\tan \left (\frac {\sqrt {c_1} (\log (x)-c_2)}{\sqrt {2}}\right )}{\sqrt {2} \sqrt {c_1}} \\ \end{align*}