Internal problem ID [15371]
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: 602.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-y^{\prime }=-5 \,{\mathrm e}^{-x} \left (\sin \left (x \right )+\cos \left (x \right )\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = -4, y^{\prime }\left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve([diff(y(x),x$2)-diff(y(x),x)=-5*exp(-x)*(sin(x)+cos(x)),y(0) = -4, D(y)(0) = 5],y(x), singsol=all)
\[ y \left (x \right ) = 2 \,{\mathrm e}^{x}-4+{\mathrm e}^{-x} \left (-2 \cos \left (x \right )+\sin \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.173 (sec). Leaf size: 28
DSolve[{y''[x]-y'[x]==-5*Exp[-x]*(Sin[x]+Cos[x]),{y[0]==-4,y'[0]==5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (2 e^x \left (e^x-2\right )+\sin (x)-2 \cos (x)\right ) \]