Internal problem ID [8203]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 623.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}}{y+x^{\frac {3}{2}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 53
dsolve(diff(y(x),x) = x^2/(y(x)+x^(3/2)),y(x), singsol=all)
\[ -2 \sqrt {33}\, \arctanh \left (\frac {\left (3 x^{\frac {3}{2}}+6 y \relax (x )\right ) \sqrt {33}}{33 x^{\frac {3}{2}}}\right )+11 \ln \left (3 y \relax (x ) x^{\frac {3}{2}}-2 x^{3}+3 y \relax (x )^{2}\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 77
DSolve[y'[x] == x^2/(x^(3/2) + y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [6 \sqrt {33} \tanh ^{-1}\left (\frac {7 x^{3/2}+3 y(x)}{\sqrt {33} \left (x^{3/2}+y(x)\right )}\right )+44 c_1=33 \left (\log \left (-\frac {3 y(x)}{2 x^{3/2}}-\frac {3 y(x)^2}{2 x^3}+1\right )+3 \log (x)\right ),y(x)\right ] \]