Internal problem ID [11778]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+2 y=10 \sin \left (4 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=10*sin(4*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-x} \cos \left (x \right ) c_{1} -\frac {7 \sin \left (4 x \right )}{13}-\frac {4 \cos \left (4 x \right )}{13} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 42
DSolve[y''[x]+2*y'[x]+2*y[x]==10*Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {7}{13} \sin (4 x)-\frac {4}{13} \cos (4 x)+c_2 e^{-x} \cos (x)+c_1 e^{-x} \sin (x) \]