Internal problem ID [15374]
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: 605.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime \prime }-y=8 \,{\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 1, y^{\prime \prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 24
dsolve([diff(y(x),x$4)-y(x)=8*exp(x),y(0) = -1, D(y)(0) = 0, (D@@2)(y)(0) = 1, (D@@3)(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x}+\left (2 x -3\right ) {\mathrm e}^{x}+\cos \left (x \right )+2 \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 28
DSolve[{y''''[x]-y[x]==8*Exp[x],{y[0]==-1,y'[0]==0,y''[0]==1,y'''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 e^x x+e^{-x}-3 e^x+2 \sin (x)+\cos (x) \]