Internal problem ID [14091]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 54.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+5*y(x)=0,y(1) = 0, D(y)(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (2 \ln \left (x \right )\right )}{2 x} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 15
DSolve[{x^2*y''[x]+3*x*y'[x]+5*y[x]==0,{y[1]==0,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sin (\log (x)) \cos (\log (x))}{x} \]