9.2.13 problem problem 25

Internal problem ID [947]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 25
Date solved : Monday, January 27, 2025 at 03:22:36 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: 0.008 (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: 0.027 (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] ==-1,Derivative[2][y][0] ==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (14 x+27 e^{-2 x/3}-23\right ) \]