71.2.15 problem 10 (c)

Internal problem ID [14347]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 10 (c)
Date solved : Tuesday, January 28, 2025 at 06:27:16 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 )&=1\\ y^{\prime }\left (2\right )&=-12 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 15

dsolve([x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=0,y(1) = 1, D(y)(2) = -12],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,{y[1]==1,Derivative[1][y][2]==-12}},y[x],x,IncludeSingularSolutions -> True]
 

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