66.2.3 problem Problem 3

Internal problem ID [13902]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 3
Date solved : Tuesday, January 28, 2025 at 06:08:04 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

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

\[ y = c_{1} +c_{2} {\mathrm e}^{\frac {\left (\sqrt {5}+3\right ) x}{2}}+c_{3} {\mathrm e}^{-\frac {\left (\sqrt {5}-3\right ) x}{2}} \]

✓ Solution by Mathematica

Time used: 0.179 (sec). Leaf size: 57

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

\[ y(x)\to \frac {1}{2} e^{-\frac {1}{2} \left (\sqrt {5}-3\right ) x} \left (\left (3+\sqrt {5}\right ) c_1-\left (\sqrt {5}-3\right ) c_2 e^{\sqrt {5} x}\right )+c_3 \]