15.10.22 problem 22

Internal problem ID [3109]
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 : 22
Date solved : Monday, January 27, 2025 at 07:19:31 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 37

dsolve(4*diff(y(x),x$3)+12*diff(y(x),x$2)-3*diff(y(x),x)+14*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_2 \,{\mathrm e}^{\frac {15 x}{4}} \sin \left (\frac {\sqrt {15}\, x}{4}\right )+c_3 \,{\mathrm e}^{\frac {15 x}{4}} \cos \left (\frac {\sqrt {15}\, x}{4}\right )+c_{1} \right ) {\mathrm e}^{-\frac {7 x}{2}} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 58

DSolve[4*D[y[x],{x,3}]+12*D[y[x],{x,2}]-3*D[y[x],x]+14*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 e^{-7 x/2}+c_2 e^{x/4} \cos \left (\frac {\sqrt {15} x}{4}\right )+c_1 e^{x/4} \sin \left (\frac {\sqrt {15} x}{4}\right ) \]