75.17.19 problem 569

Internal problem ID [16997]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Superposition principle. Exercises page 137
Problem number : 569
Date solved : Monday, March 31, 2025 at 03:37:34 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=10 \sin \left (x \right )+17 \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 34

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+5*y(x) = 10*sin(x)+17*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.268 (sec). Leaf size: 99

ode=D[y[x],{x,2}]-2*D[y[x],x]+5*y[x]==10*Sin[x]+17*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (\cos (2 x) \int _1^x-2 e^{-K[2]} \cos (K[2]) (17 \cos (K[2])+5) \sin ^2(K[2])dK[2]+\sin (2 x) \int _1^x\frac {1}{2} e^{-K[1]} \cos (2 K[1]) (10 \sin (K[1])+17 \sin (2 K[1]))dK[1]+c_2 \cos (2 x)+c_1 \sin (2 x)\right ) \]

✓ Sympy. Time used: 0.236 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 10*sin(x) - 17*sin(2*x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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