Internal problem ID [5146]
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]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=100 \sin \left (4 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{2 x} c_{1} -2 \sin \left (4 x \right )+4 \cos \left (4 x \right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 33
DSolve[y''[x]-5*y'[x]+6*y[x]==100*Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 \sin (4 x)+4 \cos (4 x)+e^{2 x} \left (c_2 e^x+c_1\right ) \]