69.1.110 problem 157

Internal problem ID [14184]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 157
Date solved : Wednesday, March 05, 2025 at 10:39:05 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

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

\[ y = \frac {\left (-x +2 c_{1} \right ) \cos \left (2 x \right )}{2}+\sin \left (2 x \right ) c_{2} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 62

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

\[ y(x)\to \sin (2 x) \int _1^x\frac {1}{2} \sin (4 K[2])dK[2]+\cos (2 x) \int _1^x-\sin ^2(2 K[1])dK[1]+c_1 \cos (2 x)+c_2 \sin (2 x) \]

✓ Sympy. Time used: 0.101 (sec). Leaf size: 19

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

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