64.13.20 problem 20

Internal problem ID [13550]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 05:52:39 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=5\\ y^{\prime }\left (1\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 15

dsolve([x^2*diff(y(x),x$2)-2*x*diff(y(x),x)-10*y(x)=0,y(1) = 5, D(y)(1) = 4],y(x), singsol=all)
 

\[ y = 2 x^{5}+\frac {3}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 16

DSolve[{x^2*D[y[x],{x,2}]-2*x*D[y[x],x]-10*y[x]==0,{y[1]==5,Derivative[1][y][1]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 x^7+3}{x^2} \]