1.9 problem Problem 15

Internal problem ID [2595]

Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number: Problem 15.
ODE order: 2.
ODE degree: 1.

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

\[ \boxed {x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y=0} \]

Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = x^{2} \left (c_{2} \ln \left (x \right )+c_{1} \right ) \]

Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 18

DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (2 c_2 \log (x)+c_1) \]