15.9.25 problem 39

Internal problem ID [3082]
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 : 39
Date solved : Monday, January 27, 2025 at 07:19:15 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)-7*diff(y(x),x$2)-8*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 35

DSolve[D[y[x],{x,4}]+2*D[y[x],{x,3}]-7*D[y[x],{x,2}]-8*D[y[x],x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (c_2 e^x+e^{4 x} \left (c_4 e^x+c_3\right )+c_1\right ) \]