Internal problem ID [13311]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients.
Additional exercises page 369
Problem number: 19.3 (c).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+26 y^{\prime \prime }+25 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = -28, y^{\prime \prime }\left (0\right ) = -102, y^{\prime \prime \prime }\left (0\right ) = 622] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(y(x),x$4)+26*diff(y(x),x$2)+25*y(x)=0,y(0) = 6, D(y)(0) = -28, (D@@2)(y)(0) = -102, (D@@3)(y)(0) = 622],y(x), singsol=all)
\[ y = -\frac {13 \sin \left (x \right )}{4}+2 \cos \left (x \right )-\frac {99 \sin \left (5 x \right )}{20}+4 \cos \left (5 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[{y''''[x]+26*y''[x]+25*y[x]==0,{y[0]==6,y'[0]==-28,y''[0]==-102,y'''[0]==622}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {13 \sin (x)}{4}-\frac {99}{20} \sin (5 x)+2 \cos (x)+4 \cos (5 x) \]