Internal problem ID [10818]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{1} +c_{2} {\mathrm e}^{\frac {\left (3+\sqrt {5}\right ) x}{2}}+c_{3} {\mathrm e}^{-\frac {\left (\sqrt {5}-3\right ) x}{2}} \]
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 57
DSolve[y'[x]+y'''[x]-3*y''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 \\ \end{align*}