Internal problem ID [11777]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=6 \sin \left (2 x \right )+7 \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=6*sin(2*x)+7*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\cos \left (2 x \right ) c_{1} +c_{2} \sin \left (2 x \right )\right ) {\mathrm e}^{-x}-\cos \left (2 x \right )+2 \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 38
DSolve[y''[x]+2*y'[x]+5*y[x]==6*Sin[2*x]+7*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (\left (-e^x+c_2\right ) \cos (2 x)+\left (2 e^x+c_1\right ) \sin (2 x)\right ) \]