13.10 problem 10

Internal problem ID [1792]

Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8.1, Singular points, Euler equations. Page 201
Problem number: 10.
ODE order: 2.
ODE degree: 1.

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

\[ \boxed {t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = 0] \end {align*}

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 14

dsolve([t^2*diff(y(t),t$2)-3*t*diff(y(t),t)+4*y(t)=0,y(1) = 1, D(y)(1) = 0],y(t), singsol=all)
 

\[ y \left (t \right ) = t^{2} \left (1-2 \ln \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 15

DSolve[{t^2*y''[t]-3*t*y'[t]+4*y[t]==0,{y[1]==1,y'[1]==0}},y[t],t,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(t)\to t^2 (1-2 \log (t)) \]