7.10.28 problem 28

Internal problem ID [298]
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 : 28
Date solved : Monday, January 27, 2025 at 02:43:25 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(2*diff(y(x),x$3)-diff(y(x),x$2)-5*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_1 \,{\mathrm e}^{3 x}+c_2 \,{\mathrm e}^{\frac {x}{2}}+c_3 \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 87

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]-5*D[y[x],x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2-5 \text {$\#$1}-2\&,2\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2-5 \text {$\#$1}-2\&,1\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2-5 \text {$\#$1}-2\&,3\right ]\right ) \]