Internal problem ID [7619]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-a y^{3}-\frac {b}{x^{\frac {3}{2}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 34
dsolve(diff(y(x),x) - a*y(x)^3 - b*x^(-3/2)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (-\ln \relax (x )+c_{1}+2 \left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3} a +\textit {\_a} +2 b}d \textit {\_a} \right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.171 (sec). Leaf size: 99
DSolve[y'[x] - a*y[x]^3 - b*x^(-3/2)==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-2 \text {RootSum}\left [-2 \text {$\#$1}^3+\text {$\#$1} \sqrt [3]{-\frac {1}{a b^2}}-2\&,\frac {\log \left (y(x) \sqrt [3]{\frac {a x^{3/2}}{b}}-\text {$\#$1}\right )}{\sqrt [3]{-\frac {1}{a b^2}}-6 \text {$\#$1}^2}\&\right ]=\frac {a x \log (x)}{\left (\frac {a x^{3/2}}{b}\right )^{2/3}}+c_1,y(x)\right ] \]