73.10.5 problem 15.2 (e)

Internal problem ID [15300]
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)
Date solved : Tuesday, January 28, 2025 at 07:51:52 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.019 (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*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0,{y[1]==0,Derivative[1][y][1]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 4 (x-1) x^2 \]