73.14.14 problem 21.13 (d)

Internal problem ID [15424]
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 (d)
Date solved : Tuesday, January 28, 2025 at 07:55:14 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 31

dsolve(diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=35*exp(5*x)+12*exp(4*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} \left (\frac {\left (35 x +7 c_{2} -5\right ) {\mathrm e}^{7 x}}{7}+c_{1} -2 \,{\mathrm e}^{6 x}\right ) \]

✓ Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==35*Exp[5*x]+12*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
 

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