Internal problem ID [13572]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 15. General solutions to Homogeneous linear differential equations. Additional
exercises page 294
Problem number: 15.5 (c).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 4, y^{\prime \prime }\left (0\right ) = 0, y^{\prime \prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 17
dsolve([diff(y(x),x$4)-y(x)=0,y(0) = 0, D(y)(0) = 4, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{-x}+{\mathrm e}^{x}+2 \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[{y''''[x]-y[x]==0,{y[0]==0,y'[0]==4,y''[0]==0,y'''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^{-x}+e^x+2 \sin (x) \]