15.9.23 problem 37

Internal problem ID [3080]
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 : 37
Date solved : Monday, January 27, 2025 at 07:19:14 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

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

\[ y = c_{1} {\mathrm e}^{\frac {x}{2}}+c_2 \,{\mathrm e}^{\frac {\left (\sqrt {3}-1\right ) x}{2}}+c_3 \,{\mathrm e}^{-\frac {\left (1+\sqrt {3}\right ) x}{2}} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 50

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

\[ y(x)\to c_1 e^{-\frac {1}{2} \left (1+\sqrt {3}\right ) x}+c_2 e^{\frac {1}{2} \left (\sqrt {3}-1\right ) x}+c_3 e^{x/2} \]