Internal problem ID [10820]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y-2=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=2,y(x), singsol=all)
\[ y \left (x \right ) = x^{3} c_{2} +c_{1} x^{2}+\frac {1}{3} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[x^2*y''[x]-4*x*y'[x]+6*y[x]==2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3}+x^2 (c_2 x+c_1) \\ \end{align*}