7.30 problem 55

Internal problem ID [186]

Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 55.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_y]]

Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+y^{\prime } x=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 10

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

\[ y \relax (x ) = c_{2} \ln \relax (x )+c_{1} \]

Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 13

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

\begin{align*} y(x)\to c_1 \log (x)+c_2 \\ \end{align*}