15.9.26 problem 40

Internal problem ID [3083]
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 : 40
Date solved : Monday, January 27, 2025 at 07:19:15 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

dsolve(diff(y(x),x$5)-3*diff(y(x),x$4)-5*diff(y(x),x$3)+15*diff(y(x),x$2)+4*diff(y(x),x)-12*y(x)=0,y(x), singsol=all)
 

\[ y = \left ({\mathrm e}^{5 x} c_{1} +c_4 \,{\mathrm e}^{4 x}+c_3 \,{\mathrm e}^{3 x}+c_5 \,{\mathrm e}^{x}+c_2 \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 42

DSolve[D[y[x],{x,5}]-3*D[y[x],{x,4}]-5*D[y[x],{x,3}]+15*D[y[x],{x,2}]+4*D[y[x],x]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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