1.3 problem 17

Internal problem ID [12576]

Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises page 14
Problem number: 17.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 15

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

\[ y \left (x \right ) = \frac {c_{2} x^{\frac {3}{2}}+c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 20

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

\[ y(x)\to \frac {c_2 x^{3/2}+c_1}{x} \]