64.3.9 problem 10

Internal problem ID [13280]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 05:14:19 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \frac {2 y^{{3}/{2}}+1}{\sqrt {x}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 36

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

\[ 2 \sqrt {2 y^{{3}/{2}}+1}\, \sqrt {x}-\int _{}^{y}\frac {1}{\sqrt {2 \textit {\_a}^{{3}/{2}}+1}}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.190 (sec). Leaf size: 54

DSolve[(2*y[x]^(3/2)+1)/x^(1/2)+(3*x^(1/2)*y[x]^(1/2)-1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {8}{3} \sqrt {x} \sqrt {2 y(x)^{3/2}+1}-\frac {4}{3} y(x) \operatorname {Hypergeometric2F1}\left (\frac {1}{2},\frac {2}{3},\frac {5}{3},-2 y(x)^{3/2}\right )=c_1,y(x)\right ] \]