Internal problem ID [4162]
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 35.20, page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)=1,y(1) = 1, D(y)(1) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \relax (x )^{2}}{2}+2 \ln \relax (x )+1 \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 17
DSolve[{x^2*y''[x]+x*y'[x]==1,{y[1]==1,y'[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \log (x) (\log (x)+4)+1 \\ \end{align*}