Internal problem ID [13364]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 21. Nonhomogeneous equations in general. Additional exercises page
391
Problem number: 21.12.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime }=1} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 3, y^{\prime \prime }\left (0\right ) = 0, y^{\prime \prime \prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve([diff(y(x),x$4)+diff(y(x),x$2)=1,y(0) = 4, D(y)(0) = 3, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 2],y(x), singsol=all)
\[ y = \frac {x^{2}}{2}+\cos \left (x \right )-2 \sin \left (x \right )+5 x +3 \]
✓ Solution by Mathematica
Time used: 0.099 (sec). Leaf size: 23
DSolve[{y''''[x]+y''[x]==1,{y[0]==4,y'[0]==3,y''[0]==0,y'''[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2}{2}+5 x-2 \sin (x)+\cos (x)+3 \]