78.2.35 problem 15.a

Internal problem ID [20987]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 2, Second order ODEs. Problems section 2.6
Problem number : 15.a
Date solved : Thursday, October 02, 2025 at 07:01:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=20 \,{\mathrm e}^{-2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 20*exp(-2*x); 
ic:=[y(0) = 0, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 5 \,{\mathrm e}^{2 x}+\frac {5 \,{\mathrm e}^{-2 x}}{3}-\frac {20 \,{\mathrm e}^{x}}{3} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 29

ode=D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==20*Exp[-2*x]; 
ic={y[0]==0,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {5 e^{-2 x}}{3}-\frac {20 e^x}{3}+5 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.149 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 20*exp(-2*x),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 5 e^{2 x} - \frac {20 e^{x}}{3} + \frac {5 e^{- 2 x}}{3} \]