64.11.28 problem 28

Internal problem ID [13399]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 28
Date solved : Wednesday, March 05, 2025 at 09:52:04 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=4 x \,{\mathrm e}^{-3 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+7*diff(y(x),x)+10*y(x) = 4*x*exp(-3*x); 
ic:=y(0) = 0, D(y)(0) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 19

ode=D[y[x],{x,2}]+7*D[y[x],x]+10*y[x]==4*x*Exp[-3*x]; 
ic={y[0]==0,Derivative[1][y][0] ==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} \left (-2 x+e^x-1\right ) \]

✓ Sympy. Time used: 0.331 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x*exp(-3*x) + 10*y(x) + 7*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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