20.7.11 problem Problem 35

Internal problem ID [3726]
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 35
Date solved : Sunday, March 30, 2025 at 02:06:37 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-10 \sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)+diff(y(x),x)-2*y(x) = -10*sin(x); 
ic:=y(0) = 2, D(y)(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.156 (sec). Leaf size: 17

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

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