35.3.14 problem 14

Internal problem ID [6118]
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
Date solved : Monday, January 27, 2025 at 01:36:28 PM
CAS classification : [_linear]

\begin{align*} x^{\prime }&=\frac {3 y^{{2}/{3}}-x}{3 y} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 11

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

\[ x \left (y \right ) = \frac {y +c_1}{y^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 15

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

\[ x(y)\to \frac {y+c_1}{\sqrt [3]{y}} \]