65.12.8 problem 19.1 (viii)

Internal problem ID [13803]
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 : 19.1 (viii)
Date solved : Tuesday, January 28, 2025 at 06:04:05 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-2\\ y^{\prime }\left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 13

dsolve([x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+5*y(x)=0,y(1) = -2, D(y)(1) = 1],y(x), singsol=all)
 

\[ y = \frac {3}{4} x^{5}-\frac {11}{4} x \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 17

DSolve[{x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+5*y[x]==0,{y[1]==-2,Derivative[1][y][1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} x \left (3 x^4-11\right ) \]