3.14 problem 14

Internal problem ID [4266]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number: 14.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {x^{\prime }-\frac {3 y^{\frac {2}{3}}-x}{3 y}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 11

dsolve(diff(x(y),y)=(3*y^(2/3)-x(y))/(3*y),x(y), singsol=all)
 

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

Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 15

DSolve[x'[y]==(3*y^(2/3)-x[y])/(3*y),x[y],y,IncludeSingularSolutions -> True]
 

\begin{align*} x(y)\to \frac {y+c_1}{\sqrt [3]{y}} \\ \end{align*}