Internal problem ID [15365]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Initial value problem. Exercises page 140
Problem number: 596.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+9 y=10 \sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve([diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=10*sin(x),y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {3 \,{\mathrm e}^{-3 x}}{5}+x \,{\mathrm e}^{-3 x}-\frac {3 \cos \left (x \right )}{5}+\frac {4 \sin \left (x \right )}{5} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 33
DSolve[{y''[x]+6*y'[x]+9*y[x]==10*Sin[x],{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} \left (5 e^{-3 x} x+3 e^{-3 x}+4 \sin (x)-3 \cos (x)\right ) \]