15.9.20 problem 34

Internal problem ID [3077]
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 : 34
Date solved : Monday, January 27, 2025 at 07:19:13 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve(2*diff(y(x),x$4)-3*diff(y(x),x$3)-20*diff(y(x),x$2)+27*diff(y(x),x)+18*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_2 \,{\mathrm e}^{6 x}+c_4 \,{\mathrm e}^{5 x}+c_{1} {\mathrm e}^{\frac {5 x}{2}}+c_3 \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 40

DSolve[2*D[y[x],{x,4}]-3*D[y[x],{x,3}]-20*D[y[x],{x,2}]+27*D[y[x],x]+18*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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