2.15 problem 10 (c)

Internal problem ID [12611]

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).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (2\right ) = -12] \end {align*}

✓ Solution by Maple

Time used: 0.0 (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)
 

\[ y \left (x \right ) = -2 x^{3}+3 x^{2} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 14

DSolve[{x^2*y''[x]-4*x*y'[x]+6*y[x]==0,{y[1]==1,y'[2]==-12}},y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

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