Internal problem ID [4166]
Book: Differential Gleichungen, Kamke, 3rd ed, Abel ODEs
Section: Abel ODE’s with constant invariant
Problem number: problem 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Abel]
\[ \boxed {-y^{3} a -\frac {b}{x^{\frac {3}{2}}}+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(-a*y(x)^3-b/(x^(3/2))+diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +2 \left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3} a +\textit {\_a} +2 b}d \textit {\_a} \right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.306 (sec). Leaf size: 320
DSolve[-a*y[x]^3-b/(x^(3/2))+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2}{3} a b^2 \text {RootSum}\left [8 \text {$\#$1}^9 a b^2+24 \text {$\#$1}^6 a b^2+24 \text {$\#$1}^3 a b^2+\text {$\#$1}^3+8 a b^2\&,\frac {4 \text {$\#$1}^6 \log \left (y(x) \sqrt [3]{\frac {a x^{3/2}}{b}}-\text {$\#$1}\right )+2 \text {$\#$1}^4 \sqrt [3]{-\frac {1}{a b^2}} \log \left (y(x) \sqrt [3]{\frac {a x^{3/2}}{b}}-\text {$\#$1}\right )+8 \text {$\#$1}^3 \log \left (y(x) \sqrt [3]{\frac {a x^{3/2}}{b}}-\text {$\#$1}\right )+\text {$\#$1}^2 \left (-\frac {1}{a b^2}\right )^{2/3} \log \left (y(x) \sqrt [3]{\frac {a x^{3/2}}{b}}-\text {$\#$1}\right )+2 \text {$\#$1} \sqrt [3]{-\frac {1}{a b^2}} \log \left (y(x) \sqrt [3]{\frac {a x^{3/2}}{b}}-\text {$\#$1}\right )+4 \log \left (y(x) \sqrt [3]{\frac {a x^{3/2}}{b}}-\text {$\#$1}\right )}{24 \text {$\#$1}^8 a b^2+48 \text {$\#$1}^5 a b^2+24 \text {$\#$1}^2 a b^2+\text {$\#$1}^2}\&\right ]=\frac {a x \log (x)}{\left (\frac {a x^{3/2}}{b}\right )^{2/3}}+c_1,y(x)\right ] \]