15.10.10 problem 10

Internal problem ID [3097]
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 : 10
Date solved : Monday, January 27, 2025 at 07:19:24 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y&=0 \end{align*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(4*diff(y(x),x$3)-8*diff(y(x),x$2)+5*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 
\[ y = \left (x c_3 +c_2 \right ) {\mathrm e}^{\frac {x}{2}}+{\mathrm e}^{x} c_{1} \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[4*D[y[x],{x,3}]-8*D[y[x],{x,2}]+5*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to e^{x/2} \left (c_2 x+c_3 e^{x/2}+c_1\right ) \]