Internal problem ID [12168]
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]]
\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y=2} \]
✓ 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)
\[ y \left (x \right ) = c_{2} x^{2}+c_{1} x^{3}+\frac {1}{3} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 21
DSolve[x^2*y''[x]-4*x*y'[x]+6*y[x]==2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^3+c_1 x^2+\frac {1}{3} \]