60.2.47 problem 623

Internal problem ID [10634]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 623
Date solved : Monday, January 27, 2025 at 09:19:00 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*}

✓ Solution by Maple

Time used: 0.141 (sec). Leaf size: 51

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

\[ -2 \sqrt {33}\, \operatorname {arctanh}\left (\frac {\left (x^{{3}/{2}}+2 y\right ) \sqrt {33}}{11 x^{{3}/{2}}}\right )+11 \ln \left (3 y x^{{3}/{2}}-2 x^{3}+3 y^{2}\right )-c_{1} = 0 \]

✓ Solution by Mathematica

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

DSolve[D[y[x],x] == x^2/(x^(3/2) + y[x]),y[x],x,IncludeSingularSolutions -> True]
 

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