15.10.3 problem 3

Internal problem ID [3090]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 3
Date solved : Monday, January 27, 2025 at 07:19:21 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

\[ y = \left (c_{1} {\mathrm e}^{\frac {5 x}{2}}+x c_3 +c_2 \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 28

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

\[ y(x)\to e^{-x} \left (c_1 e^{5 x/2}+c_3 x+c_2\right ) \]