75.17.19 problem 569

Internal problem ID [17068]
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 : Tuesday, January 28, 2025 at 09:48:56 AM
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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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