Internal problem ID [119]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}+\frac {2 y}{x^{3}}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(2*x/y(x)-3*y(x)^2/x^4+(-x^2/y(x)^2+1/y(x)^(1/2)+2*y(x)/x^3)*diff(y(x),x) = 0,y(x), singsol=all)
\[ \frac {y \relax (x )^{2}}{x^{3}}+\frac {x^{2}}{y \relax (x )}+2 \sqrt {y \relax (x )}+c_{1} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[2*x/y[x]-3*y[x]^2/x^4+(-x^2/y[x]^2+1/y[x]^(1/2)+2*y[x]/x^3)*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved