73.15.4 problem 22.1 (d)

Internal problem ID [15356]
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 : Thursday, March 13, 2025 at 05:55:55 AM
CAS classification : [[_2nd_order, _missing_y]]

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

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

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x) = exp(1/2*x); 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.200 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x/2) + 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- 3 x} + \frac {4 e^{\frac {x}{2}}}{7} \]