8.25 problem 25

Internal problem ID [4380]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number: 25.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {3 x^{2} y+y^{\prime } x^{3}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2] \end {align*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 9

dsolve([3*x^2*y(x)+x^3*diff(y(x),x)=0,y(1) = 2],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {2}{x^{3}} \]

Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 10

DSolve[{3*x^2*y[x]+x^3*y'[x]==0,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2}{x^3} \\ \end{align*}