Internal problem ID [14742]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number: 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +4 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = -1, y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 11
dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=0,y(1) = -1, D(y)(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\cos \left (2 \ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 12
DSolve[{x^2*y''[x]+x*y'[x]+4*y[x]==0,{y[1]==-1,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\cos (2 \log (x)) \]