Internal problem ID [5157]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=3 \sin \left (x \right )} \] With initial conditions \begin {align*} \left [y \left (0\right ) = -{\frac {9}{10}}, y^{\prime }\left (0\right ) = -{\frac {7}{10}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=3*sin(x),y(0) = -9/10, D(y)(0) = -7/10],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x}-\frac {9 \cos \left (x \right )}{10}+\frac {3 \sin \left (x \right )}{10}-{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 30
DSolve[{y''[x]+3*y'[x]+2*y[x]==3*Sin[x],{y[0]==-9/10,y'[0]==-7/10}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^{-2 x} \left (e^x-1\right )+\frac {3 \sin (x)}{10}-\frac {9 \cos (x)}{10} \]