20.1.11 problem Problem 17

Internal problem ID [3568]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 17
Date solved : Monday, January 27, 2025 at 07:44:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=9 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 18

dsolve(2*x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=9*x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 23

DSolve[2*x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==9*x^2,y[x],x,IncludeSingularSolutions -> True]
 

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