78.9.3 problem 3 (a and b)

Internal problem ID [18251]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 14. Introduction. Problems at page 112
Problem number : 3 (a and b)
Date solved : Tuesday, January 28, 2025 at 11:44:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 26

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

\[ y(x)\to -2 x+c_1 e^{-x}+c_2 e^{2 x}+1 \]