23.2.23 problem 8

Internal problem ID [4140]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 8
Date solved : Monday, January 27, 2025 at 08:39:55 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 22

dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=x^2+2,y(x), singsol=all)
 

\[ y \left (x \right ) = \ln \left (x \right ) x^{2}+1+x^{2} \left (c_{1} -1\right )+c_{2} x \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 25

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

\[ y(x)\to x^2 \log (x)+(-1+c_2) x^2+c_1 x+1 \]