73.14.13 problem 21.13 (c)

Internal problem ID [15423]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.13 (c)
Date solved : Tuesday, January 28, 2025 at 07:55:12 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 31

dsolve(diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=-18*exp(4*x)+14*exp(5*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} \left (\frac {\left (14 x +7 c_{2} -2\right ) {\mathrm e}^{7 x}}{7}+c_{1} +3 \,{\mathrm e}^{6 x}\right ) \]

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==-18*Exp[4*x]+14*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 e^{4 x}+c_1 e^{-2 x}+e^{5 x} \left (2 x-\frac {2}{7}+c_2\right ) \]