78.13.1 problem 1 (a)

Internal problem ID [18323]
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 18. The Method of Undetermined Coefficients. Problems at page 132
Problem number : 1 (a)
Date solved : Tuesday, January 28, 2025 at 11:46:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)+3*diff(y(x),x)-10*y(x)=6*exp(4*x),y(x), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{9 x}+3 \,{\mathrm e}^{7 x} c_{2} +3 c_{1} \right ) {\mathrm e}^{-5 x}}{3} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}] +3*D[y[x],x]-10*y[x]==6*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{4 x}}{3}+c_1 e^{-5 x}+c_2 e^{2 x} \]