Internal problem ID [4642]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Further problems 25. page 1094
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+4 y-2 \left (\cos ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=2*cos(x)^2,y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-2 x}+{\mathrm e}^{-2 x} x c_{1}+\frac {1}{4}+\frac {\sin \left (2 x \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 29
DSolve[y''[x]+4*y'[x]+4*y[x]==2*Cos[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} \left (\sin (2 x)+8 e^{-2 x} (c_2 x+c_1)+2\right ) \\ \end{align*}