20.7.10 problem Problem 34

Internal problem ID [3725]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 34
Date solved : Tuesday, March 04, 2025 at 05:08:46 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=9 x \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=7 \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)-y(x) = 9*x*exp(2*x); 
ic:=y(0) = 0, D(y)(0) = 7; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y \left (x \right ) = 8 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{-x}+\left (3 x -4\right ) {\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 29

ode=D[y[x],{x,2}]-y[x]==9*x*Exp[2*x]; 
ic={y[0]==0,Derivative[1][y][0] ==7}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} (3 x-4)-4 e^{-x}+8 e^x \]

✓ Sympy. Time used: 0.113 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*x*exp(2*x) - y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 7} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (3 x - 4\right ) e^{2 x} + 8 e^{x} - 4 e^{- x} \]