64.9.7 problem 8

Internal problem ID [13405]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 124
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 05:41:50 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

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

\[ y = {\mathrm e}^{2 x} c_{1} +{\mathrm e}^{x} c_{2} +2 x^{2}+6 x +7 \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 29

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

\[ y(x)\to 2 x^2+6 x+c_1 e^x+c_2 e^{2 x}+7 \]