60.2.47 problem 623

Internal problem ID [10621]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 623
Date solved : Sunday, March 30, 2025 at 06:11:01 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {x^{2}}{y+x^{{3}/{2}}} \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 51

ode:=diff(y(x),x) = x^2/(y(x)+x^(3/2)); 
dsolve(ode,y(x), singsol=all);
 

\[ -2 \sqrt {33}\, \operatorname {arctanh}\left (\frac {\left (x^{{3}/{2}}+2 y\right ) \sqrt {33}}{11 x^{{3}/{2}}}\right )+11 \ln \left (3 x^{{3}/{2}} y-2 x^{3}+3 y^{2}\right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.141 (sec). Leaf size: 77

ode=D[y[x],x] == x^2/(x^(3/2) + y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [6 \sqrt {33} \text {arctanh}\left (\frac {7 x^{3/2}+3 y(x)}{\sqrt {33} \left (x^{3/2}+y(x)\right )}\right )+44 c_1=33 \left (\log \left (-\frac {3 y(x)}{2 x^{3/2}}-\frac {3 y(x)^2}{2 x^3}+1\right )+3 \log (x)\right ),y(x)\right ] \]

✓ Sympy. Time used: 29.688 (sec). Leaf size: 66

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2/(x**(3/2) + y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + \frac {3 \log {\left (x \right )}}{2} + \frac {\left (11 - \sqrt {33}\right ) \log {\left (\frac {1}{2} + \frac {\sqrt {33}}{6} + \frac {y{\left (x \right )}}{x^{\frac {3}{2}}} \right )}}{22} + \frac {\left (\sqrt {33} + 11\right ) \log {\left (- \frac {\sqrt {33}}{6} + \frac {1}{2} + \frac {y{\left (x \right )}}{x^{\frac {3}{2}}} \right )}}{22} = 0 \]