15.9.28 problem 42

Internal problem ID [3085]
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 : 42
Date solved : Monday, January 27, 2025 at 07:19:16 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 35

dsolve(diff(y(x),x$5)+3*diff(y(x),x$4)-15*diff(y(x),x$3)-19*diff(y(x),x$2)+30*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \left (c_2 \,{\mathrm e}^{8 x}+c_4 \,{\mathrm e}^{6 x}+{\mathrm e}^{5 x} c_{1} +c_3 \,{\mathrm e}^{3 x}+c_5 \right ) {\mathrm e}^{-5 x} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 47

DSolve[D[y[x],{x,5}]+3*D[y[x],{x,4}]-15*D[y[x],{x,3}]-19*D[y[x],{x,2}]+30*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{5} c_1 e^{-5 x}-\frac {1}{2} c_2 e^{-2 x}+c_3 e^x+\frac {1}{3} c_4 e^{3 x}+c_5 \]