67.2.26 problem Problem 3(d)

Internal problem ID [13983]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 3(d)
Date solved : Tuesday, January 28, 2025 at 06:11:00 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 41

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

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

✓ Solution by Mathematica

Time used: 0.368 (sec). Leaf size: 71

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

\[ y(x)\to \int _1^x\left (e^{-K[1]} c_3+e^{\frac {K[1]}{2}} c_2 \cos \left (\frac {K[1]}{2 \sqrt {3}}\right )+e^{\frac {K[1]}{2}} c_1 \sin \left (\frac {K[1]}{2 \sqrt {3}}\right )\right )dK[1]+c_4 \]