Internal problem ID [4638]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-5 y^{\prime }+6 y-100 \sin \left (4 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=100*sin(4*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x}-2 \sin \left (4 x \right )+4 \cos \left (4 x \right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 33
DSolve[y''[x]-5*y'[x]+6*y[x]==100*Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \sin (4 x)+4 \cos (4 x)+e^{2 x} \left (c_2 e^x+c_1\right ) \\ \end{align*}