Internal problem ID [7913]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 333.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\left (2 x^{\frac {5}{2}} y^{\frac {3}{2}}+y x^{2}-x \right ) y^{\prime }-x^{\frac {3}{2}} y^{\frac {5}{2}}+x y^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve((2*x^(5/2)*y(x)^(3/2)+x^2*y(x)-x)*diff(y(x),x)-x^(3/2)*y(x)^(5/2)+x*y(x)^2-y(x) = 0,y(x), singsol=all)
\[ 3 \ln \left (y \relax (x )\right )+\frac {1}{x^{\frac {3}{2}} y \relax (x )^{\frac {3}{2}}}-\frac {3}{\sqrt {x}\, \sqrt {y \relax (x )}}-\frac {3 \ln \relax (x )}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.553 (sec). Leaf size: 72
DSolve[-y[x] + x*y[x]^2 - x^(3/2)*y[x]^(5/2) + (-x + x^2*y[x] + 2*x^(5/2)*y[x]^(3/2))*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2 \sqrt {x y(x)} \log (y(x))}{\sqrt {x} \sqrt {y(x)}}-\frac {\sqrt {x y(x)} \left (3 x^{3/2} y(x)^{3/2} \log (x)+6 x y(x)-2\right )}{3 x^2 y(x)^2}=c_1,y(x)\right ] \]