28.2.27 problem 27

Internal problem ID [4470]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 27
Date solved : Sunday, March 30, 2025 at 03:23:25 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=36 x \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-2*y(x) = 36*x*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (6 x^{2}+c_2 -4 x \right ) {\mathrm e}^{2 x}+{\mathrm e}^{-x} c_1 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 34

ode=D[y[x],{x,2}]-D[y[x],x]-2*y[x]==36*x*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} \left (6 x^2-4 x+\frac {4}{3}+c_2\right )+c_1 e^{-x} \]

✓ Sympy. Time used: 0.237 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-36*x*exp(2*x) - 2*y(x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{- x} + \left (C_{1} + 6 x^{2} - 4 x\right ) e^{2 x} \]