Internal problem ID [10092]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-1 Equation of form
\(y''+f(x)y'+g(x)y=0\)
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+a y^{\prime }+b y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(diff(y(x),x$2)+a*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\left (-\frac {a}{2}+\frac {\sqrt {a^{2}-4 b}}{2}\right ) x}+c_{2} {\mathrm e}^{\left (-\frac {a}{2}-\frac {\sqrt {a^{2}-4 b}}{2}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 47
DSolve[y''[x]+a*y'[x]+b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\frac {1}{2} x \left (\sqrt {a^2-4 b}+a\right )} \left (c_2 e^{x \sqrt {a^2-4 b}}+c_1\right ) \\ \end{align*}