64.11.25 problem 25

Internal problem ID [13396]
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 : 25
Date solved : Wednesday, March 05, 2025 at 09:51:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=9 x^{2}+4 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+3*y(x) = 9*x^2+4; 
ic:=y(0) = 6, D(y)(0) = 8; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -6 \,{\mathrm e}^{x}+2 \,{\mathrm e}^{3 x}+3 x^{2}+8 x +10 \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-4*D[y[x],x]+3*y[x]==9*x^2+4; 
ic={y[0]==6,Derivative[1][y][0] ==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 3 x^2+8 x-6 e^x+2 e^{3 x}+10 \]

✓ Sympy. Time used: 0.189 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*x**2 + 3*y(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 4,0) 
ics = {y(0): 6, Subs(Derivative(y(x), x), x, 0): 8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 x^{2} + 8 x + 2 e^{3 x} - 6 e^{x} + 10 \]