Internal problem ID [13251]
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 (a).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 8, y^{\prime \prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(y(x),x$3)+4*diff(y(x),x)=0,y(0) = 3, D(y)(0) = 8, (D@@2)(y)(0) = 4],y(x), singsol=all)
\[ y = 4+4 \sin \left (2 x \right )-\cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 19
DSolve[{y'''[x]+4*y'[x]==0,{y[0]==3,y'[0]==8,y''[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 4 \sin (2 x)-\cos (2 x)+4 \]