Internal problem ID [12485]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.3, page 255
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=2 \sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = -2, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 14
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+y(x)=2*sin(x),y(0) = -2, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \left (3 x -3\right ) {\mathrm e}^{x}+\cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 16
DSolve[{y''[x]-2*y'[x]+y[x]==2*Sin[x],{y[0]==-2,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 e^x (x-1)+\cos (x) \]