15.10.20 problem 20

Internal problem ID [3107]
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 : 20
Date solved : Monday, January 27, 2025 at 07:19:30 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

dsolve(2*diff(y(x),x$3)-3*diff(y(x),x$2)+11*diff(y(x),x)-40*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {5 x}{2}}+c_2 \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {31}\, x}{2}\right )+c_3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {31}\, x}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 50

DSolve[2*D[y[x],{x,3}]-3*D[y[x],{x,2}]+11*D[y[x],x]-40*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/2} \left (c_3 e^{3 x}+c_2 \cos \left (\frac {\sqrt {31} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {31} x}{2}\right )\right ) \]