73.15.72 problem 22.14 (c)

Internal problem ID [15432]
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 : 22.14 (c)
Date solved : Monday, March 31, 2025 at 01:37:27 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=5 \sin \left (x \right )^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+5*y(x) = 5*sin(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_2 +{\mathrm e}^{2 x} \cos \left (x \right ) c_1 +\frac {1}{2}+\frac {4 \sin \left (2 x \right )}{13}-\frac {\cos \left (2 x \right )}{26} \]

✓ Mathematica. Time used: 0.138 (sec). Leaf size: 71

ode=D[y[x],{x,2}]-4*D[y[x],x]+5*y[x]==5*Sin[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} \left (\cos (x) \int _1^x-5 e^{-2 K[2]} \sin ^3(K[2])dK[2]+\sin (x) \int _1^x5 e^{-2 K[1]} \cos (K[1]) \sin ^2(K[1])dK[1]+c_2 \cos (x)+c_1 \sin (x)\right ) \]

✓ Sympy. Time used: 0.875 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )}\right ) e^{2 x} + \frac {4 \sin {\left (2 x \right )}}{13} - \frac {\cos {\left (2 x \right )}}{26} + \frac {1}{2} \]