73.15.10 problem 22.4

Internal problem ID [15370]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.4
Date solved : Monday, March 31, 2025 at 01:35:45 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-4 \cos \left (x \right )+7 \sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=-5 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)-10*y(x) = -4*cos(x)+7*sin(x); 
ic:=y(0) = 8, D(y)(0) = -5; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 6 \,{\mathrm e}^{-2 x}+\frac {3 \,{\mathrm e}^{5 x}}{2}+\frac {\cos \left (x \right )}{2}-\frac {\sin \left (x \right )}{2} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 30

ode=D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==-4*Cos[x]+7*Sin[x]; 
ic={y[0]==8,Derivative[1][y][0] ==-5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} \left (3 e^{-2 x} \left (e^{7 x}+4\right )-\sin (x)+\cos (x)\right ) \]

✓ Sympy. Time used: 0.274 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*y(x) - 7*sin(x) + 4*cos(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 8, Subs(Derivative(y(x), x), x, 0): -5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 e^{5 x}}{2} - \frac {\sin {\left (x \right )}}{2} + \frac {\cos {\left (x \right )}}{2} + 6 e^{- 2 x} \]