Internal problem ID [10565]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number: 6(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y+8 \sin \left (2 x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=-8*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x} c_{1} -\cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 25
DSolve[y''[x]-4*y'[x]+4*y[x]==-8*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\cos (2 x)+e^{2 x} (c_2 x+c_1) \\ \end{align*}