88.10.10 problem 10

Internal problem ID [24045]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 52
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:55:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 y^{\prime \prime }-4 y^{\prime }+y&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=3*diff(diff(y(x),x),x)-4*diff(y(x),x)+y(x) = exp(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 31

ode=3*D[y[x],{x,2}]-4*D[y[x],x]+y[x]==Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{x/3}+e^x \left (\frac {x}{2}-\frac {3}{4}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - exp(x) - 4*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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