39.1.1 problem Problem 11.1

Internal problem ID [6506]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number : Problem 11.1
Date solved : Monday, January 27, 2025 at 02:09:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

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

\[ y = c_2 \,{\mathrm e}^{-x}+{\mathrm e}^{2 x} c_1 -2 x^{2}+2 x -3 \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 31

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

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