71.2.14 problem 10 (b)

Internal problem ID [14346]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 10 (b)
Date solved : Tuesday, January 28, 2025 at 06:27:13 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 (2\right )&=4\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 14

DSolve[{x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0,{Derivative[1][y][1]==0,y[2]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (2 x-3) \]