73.15.4 problem 22.1 (d)

Internal problem ID [15435]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.1 (d)
Date solved : Tuesday, January 28, 2025 at 07:55:35 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{\frac {x}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)+3*diff(y(x),x)=exp(x/2),y(x), singsol=all)
 

\[ y = -\frac {\left (-3 \,{\mathrm e}^{3 x} c_{2} +c_{1} -\frac {12 \,{\mathrm e}^{\frac {7 x}{2}}}{7}\right ) {\mathrm e}^{-3 x}}{3} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]+3*D[y[x],x]==30*Exp[x/2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {120 e^{x/2}}{7}-\frac {1}{3} c_1 e^{-3 x}+c_2 \]