Internal problem ID [13663]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-11 y^{\prime } x +36 y=0} \] With initial conditions \begin {align*} \left [y \left (1\right ) = {\frac {1}{2}}, y^{\prime }\left (1\right ) = 2\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = x^{6} \left (\frac {1}{2}-\ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 18
DSolve[{x^2*y''[x]-11*x*y'[x]+36*y[x]==0,{y[1]==1/2,y'[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x^6 (1-2 \log (x)) \]