29.15.1 problem 409

Internal problem ID [5007]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 409
Date solved : Monday, January 27, 2025 at 10:02:45 AM
CAS classification : [_quadrature]

\begin{align*} X^{{2}/{3}} y^{\prime }&=Y^{{2}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 20

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

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