71.2.13 problem 10 (a)

Internal problem ID [14345]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 10 (a)
Date solved : Tuesday, January 28, 2025 at 06:27:11 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 \left (2\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.068 (sec). Leaf size: 13

dsolve([x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=0,y(1) = 0, y(2) = -4],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.012 (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,y[2]==-4}},y[x],x,IncludeSingularSolutions -> True]
 

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