73.13.21 problem 20.2 (c)

Internal problem ID [15399]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 20. Euler equations. Additional exercises page 382
Problem number : 20.2 (c)
Date solved : Tuesday, January 28, 2025 at 07:54:28 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-11 x y^{\prime }+36 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

dsolve([x^2*diff(y(x),x$2)-11*x*diff(y(x),x)+36*y(x)=0,y(1) = 1/2, D(y)(1) = 2],y(x), singsol=all)
 

\[ y = x^{6} \left (\frac {1}{2}-\ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 18

DSolve[{x^2*D[y[x],{x,2}]-11*x*D[y[x],x]+36*y[x]==0,{y[1]==1/2,Derivative[1][y][1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^6 (1-2 \log (x)) \]