Internal problem ID [5140]
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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=4 \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=4*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{x}+2 \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 21
DSolve[y''[x]-2*y'[x]+y[x]==4*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 \cos (x)+e^x (c_2 x+c_1) \]