20.6.17 problem Problem 39

Internal problem ID [3712]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 39
Date solved : Monday, January 27, 2025 at 07:55:46 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=4 x^{2}+5 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 38

dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=4*x^2+5,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (-4 x^{2}-4 x -11\right ) {\mathrm e}^{-2 x} {\mathrm e}^{2 x}}{2}+\left (c_{2} {\mathrm e}^{3 x}+c_{1} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]+D[y[x],x]-2*y[x]==4*x^2+5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 x^2-2 x+c_1 e^{-2 x}+c_2 e^x-\frac {11}{2} \]