65.12.11 problem 19.2

Internal problem ID [13806]
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
Date solved : Tuesday, January 28, 2025 at 06:04:15 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} a y^{\prime \prime }+\left (b -a \right ) y^{\prime }+c y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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: 0.044 (sec). Leaf size: 72

DSolve[a*D[y[z],{z,2}]+(b-a)*D[y[z],z]+c*y[z]==0,y[z],z,IncludeSingularSolutions -> True]
 

\[ y(z)\to \left (c_2 e^{\frac {z \sqrt {a^2-2 a (b+2 c)+b^2}}{a}}+c_1\right ) \exp \left (-\frac {z \left (\sqrt {a^2-2 a (b+2 c)+b^2}-a+b\right )}{2 a}\right ) \]