Internal problem ID [14768]
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: 59.
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 ) = 0, y^{\prime }\left (-1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 28
dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=0,y(-1) = 0, D(y)(-1) = 2],y(x), singsol=all)
\[ y \left (x \right ) = -\cosh \left (2 \pi \right ) \sin \left (2 \ln \left (x \right )\right )+i \sinh \left (2 \pi \right ) \cos \left (2 \ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 20
DSolve[{x^2*y''[x]+x*y'[x]+4*y[x]==0,{y[-1]==0,y'[-1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to i \sinh (2 (\pi +i \log (x))) \]