84.4.2 problem 2.12

Internal problem ID [22087]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 2. Solutions. Supplementary problems
Problem number : 2.12
Date solved : Thursday, October 02, 2025 at 08:23:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = {\mathrm e}^{2 x} \left (c_1 x +c_2 \right )+{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to e^x \left (1+e^x (c_2 x+c_1)\right ) \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 15

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

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