66.2.5 problem Problem 5

Internal problem ID [13904]
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
Date solved : Tuesday, January 28, 2025 at 06:08:07 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=2 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = c_{2} x^{2}+c_{1} x^{3}+\frac {1}{3} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 21

DSolve[x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^3+c_1 x^2+\frac {1}{3} \]