71.2.17 problem 10 (e)

Internal problem ID [14349]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 10 (e)
Date solved : Tuesday, January 28, 2025 at 06:27:20 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 (0\right )&=0\\ y \left (2\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 15

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

\[ y = x^{2} \left (1+c_{1} \left (x -2\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 23

DSolve[{x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0,{y[0]==0,y[2]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^2 (x-c_1 x+2 c_1) \]