Internal problem ID [13312]
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 (d).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+9 y^{\prime \prime }+9 y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 10, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 6, y^{\prime \prime \prime }\left (0\right ) = -60] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve([diff(y(x),x$4)+diff(y(x),x$3)+9*diff(y(x),x$2)+9*diff(y(x),x)=0,y(0) = 10, D(y)(0) = 0, (D@@2)(y)(0) = 6, (D@@3)(y)(0) = -60],y(x), singsol=all)
\[ y = 4+6 \,{\mathrm e}^{-x}+2 \sin \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 20
DSolve[{y''''[x]+y'''[x]+9*y''[x]+9*y'[x]==0,{y[0]==10,y'[0]==0,y''[0]==6,y'''[0]==-60}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 6 e^{-x}+2 \sin (3 x)+4 \]