7.10.25 problem 25

Internal problem ID [295]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 25
Date solved : Monday, January 27, 2025 at 02:43:24 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime }+2 y^{\prime \prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 15

dsolve([3*diff(y(x),x$3)+2*diff(y(x),x$2)=0,y(0) = -1, D(y)(0) = 0, (D@@2)(y)(0) = 1],y(x), singsol=all)
 

\[ y = -\frac {13}{4}+\frac {3 x}{2}+\frac {9 \,{\mathrm e}^{-\frac {2 x}{3}}}{4} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 23

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

\[ y(x)\to \frac {1}{4} \left (6 x+9 e^{-2 x/3}-13\right ) \]