Internal problem ID [8613]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1035.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+y^{\prime } a +y b=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(diff(diff(y(x),x),x)+a*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\left (-\frac {a}{2}+\frac {\sqrt {a^{2}-4 b}}{2}\right ) x}+c_{2} {\mathrm e}^{\left (-\frac {a}{2}-\frac {\sqrt {a^{2}-4 b}}{2}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 47
DSolve[b*y[x] + a*y'[x] + 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*}