73.10.12 problem 15.5 (a)

Internal problem ID [15307]
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)
Date solved : Tuesday, January 28, 2025 at 07:52:06 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=0 \end{align*}

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: 0.020 (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: 60.012 (sec). Leaf size: 53

DSolve[{D[y[x],{x,3}]+4*D[y[x],x]==0,{y[0]==3,Derivative[1][y][0] ==8,Derivative[2][y][0] ==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x2 (4 \cos (2 K[1])+\sin (2 K[1]))dK[1]-\int _1^02 (4 \cos (2 K[1])+\sin (2 K[1]))dK[1]+3 \]