15.9.21 problem 35

Internal problem ID [3078]
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 : 35
Date solved : Monday, January 27, 2025 at 07:19:13 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 12 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(12*diff(y(x),x$4)-4*diff(y(x),x$3)-3*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \left (c_2 \,{\mathrm e}^{x}+c_4 \,{\mathrm e}^{\frac {5 x}{6}}+c_{1} {\mathrm e}^{\frac {x}{2}}+c_3 \right ) {\mathrm e}^{-\frac {x}{2}} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 39

DSolve[12*D[y[x],{x,4}]-4*D[y[x],{x,3}]-3*D[y[x],{x,2}]+D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/2} \left (3 c_1 e^{5 x/6}+2 c_3 e^x-2 c_2\right )+c_4 \]