32.9.18 problem Exercise 22, problem 18, page 240

Internal problem ID [5992]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number : Exercise 22, problem 18, page 240
Date solved : Monday, January 27, 2025 at 01:30:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=x^3,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{2}}{x^{2}}+c_{1} x^{2}+\frac {x^{3}}{5} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 25

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-4*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3}{5}+c_2 x^2+\frac {c_1}{x^2} \]