15.10.8 problem 8

Internal problem ID [3095]
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 : 8
Date solved : Monday, January 27, 2025 at 07:19:23 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 4 y^{\left (5\right )}-3 y^{\prime \prime \prime }-y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(4*diff(y(x),x$5)-3*diff(y(x),x$3)-diff(y(x),x$2)=0,y(x), singsol=all)
 

\[ y = \left (x c_5 +c_4 \right ) {\mathrm e}^{-\frac {x}{2}}+c_2 x +c_3 \,{\mathrm e}^{x}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.086 (sec). Leaf size: 36

DSolve[4*D[y[x],{x,5}]-3*D[y[x],{x,3}]-D[y[x],{x,2}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 4 e^{-x/2} (c_2 (x+4)+c_1)+c_3 e^x+c_5 x+c_4 \]