67.15.4 problem 22.1 (d)

Internal problem ID [16722]
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, October 02, 2025 at 01:38:10 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y = -\frac {{\mathrm e}^{-3 x} c_1}{3}+\frac {4 \,{\mathrm e}^{\frac {x}{2}}}{7}+c_2 \]

✓ Mathematica. Time used: 0.051 (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]
 

\begin{align*} y(x)&\to \frac {120 e^{x/2}}{7}-\frac {1}{3} c_1 e^{-3 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.111 (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)
 

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