Internal problem ID [10722]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 19, CauchyEuler equations. Exercises page 174
Problem number: 19.2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {a y^{\prime \prime }+\left (-a +b \right ) y^{\prime }+c y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 67
dsolve(a*diff(y(z),z$2)+(b-a)*diff(y(z),z)+c*y(z)=0,y(z), singsol=all)
\[ y \left (z \right ) = c_{1} {\mathrm e}^{\frac {\left (-b +a +\sqrt {a^{2}-2 b a -4 c a +b^{2}}\right ) z}{2 a}}+c_{2} {\mathrm e}^{-\frac {\left (b -a +\sqrt {a^{2}-2 b a -4 c a +b^{2}}\right ) z}{2 a}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 66
DSolve[a*y''[z]+(b-a)*y'[z]+c*y[z]==0,y[z],z,IncludeSingularSolutions -> True]
\begin{align*} y(z)\to e^{-\frac {z \left (\sqrt {(a-b)^2-4 a c}-a+b\right )}{2 a}} \left (c_2 e^{\frac {z \sqrt {(a-b)^2-4 a c}}{a}}+c_1\right ) \\ \end{align*}