7.5.41 problem 41

Internal problem ID [145]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 41
Date solved : Friday, February 07, 2025 at 07:57:56 AM
CAS classification : [_exact, _rational]

\begin{align*} \frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 35

dsolve(( 2*x/y(x) - 3*y(x)^2/x^4 )+( 2*y(x)/x^3-x^2/y(x)^2+1/sqrt(y(x)) )*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \frac {2 y^{{3}/{2}} x^{3}+c_1 \,x^{3} y+x^{5}+y^{3}}{x^{3} y} = 0 \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(  2*x/y[x] -3*y[x]^2/x^4 )+( 2*y[x]/x^3 -x^2/y[x]^2 + 1/Sqrt[y[x]] )*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved