Internal problem ID [4632]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Test Excercise 25. page 1093
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+y-4 \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=4*sin(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{x} c_{1} x +2 \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 21
DSolve[y''[x]-2*y'[x]+y[x]==4*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \cos (x)+e^x (c_2 x+c_1) \\ \end{align*}