Internal problem ID [12070]
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]]
\[ \boxed {a y^{\prime \prime }+\left (b -a \right ) y^{\prime }+c y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 69
dsolve(a*diff(y(z),z$2)+(b-a)*diff(y(z),z)+c*y(z)=0,y(z), singsol=all)
\[ y \left (z \right ) = c_{1} {\mathrm e}^{\frac {\left (a -b +\sqrt {a^{2}+\left (-2 b -4 c \right ) a +b^{2}}\right ) z}{2 a}}+{\mathrm e}^{-\frac {\left (-a +b +\sqrt {a^{2}+\left (-2 b -4 c \right ) a +b^{2}}\right ) z}{2 a}} c_{2} \]
✓ Solution by Mathematica
Time used: 0.073 (sec). Leaf size: 72
DSolve[a*y''[z]+(b-a)*y'[z]+c*y[z]==0,y[z],z,IncludeSingularSolutions -> True]
\[ y(z)\to \left (c_2 e^{\frac {z \sqrt {a^2-2 a (b+2 c)+b^2}}{a}}+c_1\right ) \exp \left (-\frac {z \left (\sqrt {a^2-2 a (b+2 c)+b^2}-a+b\right )}{2 a}\right ) \]