37.1.8 problem 10.2.11 (ii)

Internal problem ID [6395]
Book : Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section : Chapter 10, Differential equations. Section 10.2, ODEs with constant Coefficients. page 307
Problem number : 10.2.11 (ii)
Date solved : Sunday, March 30, 2025 at 10:54:23 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=2 \cos \left (x \right ) \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 11

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 2*cos(x); 
ic:=y(0) = 1, D(y)(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{x}-\sin \left (x \right ) \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 13

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

\[ y(x)\to e^x-\sin (x) \]

✓ Sympy. Time used: 0.192 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = e^{x} - \sin {\left (x \right )} \]