7.10.24 problem 24

Internal problem ID [294]
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 : 24
Date solved : Monday, January 27, 2025 at 02:43:24 AM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 18

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

\[ y = -\frac {7}{2}+\frac {{\mathrm e}^{2 x}}{2}+4 \,{\mathrm e}^{-\frac {x}{2}} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 25

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

\[ y(x)\to \frac {1}{2} \left (8 e^{-x/2}+e^{2 x}-7\right ) \]