73.14.12 problem 21.13 (b)

Internal problem ID [15422]
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 (b)
Date solved : Tuesday, January 28, 2025 at 07:55:10 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&={\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 31

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

\[ y(x)\to c_1 e^{-2 x}+e^{5 x} \left (\frac {x}{7}-\frac {1}{49}+c_2\right ) \]