Internal problem ID [8669]
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]
\[ \boxed {\left (2 x^{\frac {5}{2}} y^{\frac {3}{2}}+y x^{2}-x \right ) y^{\prime }-x^{\frac {3}{2}} y^{\frac {5}{2}}+x y^{2}-y=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 38
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)
\[ -\frac {3 \left (\frac {\left (c_{1} +\frac {3 \ln \left (x \right )}{2}-3 \ln \left (y \left (x \right )\right )\right ) x^{\frac {3}{2}} y \left (x \right )^{\frac {3}{2}}}{3}+x y \left (x \right )-\frac {1}{3}\right )}{x^{\frac {3}{2}} y \left (x \right )^{\frac {3}{2}}} = 0 \]
✓ Solution by Mathematica
Time used: 0.313 (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]
\[ \text {Solve}\left [\frac {2 \sqrt {x y(x)} \log (y(x))}{\sqrt {x} \sqrt {y(x)}}-\frac {\sqrt {x y(x)} \left (3 x^{3/2} y(x)^{3/2} \log (x)+6 x y(x)-2\right )}{3 x^2 y(x)^2}=c_1,y(x)\right ] \]