15.9.13 problem 27

Internal problem ID [3070]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 27
Date solved : Monday, January 27, 2025 at 07:19:10 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)+diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{3 x}+{\mathrm e}^{2 x} c_2 +c_3 \,{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

DSolve[D[y[x],{x,3}]-4*D[y[x],{x,2}]+D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (e^{3 x} \left (c_3 e^x+c_2\right )+c_1\right ) \]