Internal problem ID [13244]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 15. General solutions to Homogeneous linear differential equations. Additional
exercises page 294
Problem number: 15.2 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=0,y(1) = 0, D(y)(1) = 4],y(x), singsol=all)
\[ y = 4 x^{3}-4 x^{2} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 13
DSolve[{x^2*y''[x]-4*x*y'[x]+6*y[x]==0,{y[1]==0,y'[1]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 4 (x-1) x^2 \]