Internal problem ID [7626]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 45.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Abel]
Solve \begin {gather*} \boxed {y^{\prime }+2 \left (x^{3} a^{2}-b^{2} x \right ) y^{3}+3 b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 123
dsolve(diff(y(x),x) + 2*(a^2*x^3 - b^2*x)*y(x)^3 + 3*b*y(x)^2=0,y(x), singsol=all)
\[ c_{1}+\frac {\left (\left (\frac {a x}{b}+\frac {1}{\frac {b^{2} y \relax (x )}{a}-\frac {b}{a x}}\right )^{2}-1\right )^{\frac {1}{4}}}{\left (\frac {b^{2} y \relax (x )}{a}-\frac {b}{a x}\right ) \sqrt {\frac {a x}{b}+\frac {1}{\frac {b^{2} y \relax (x )}{a}-\frac {b}{a x}}}}-\left (\int _{}^{\frac {a \,x^{2} y \relax (x )}{b x y \relax (x )-1}}\frac {\left (\textit {\_a}^{2}-1\right )^{\frac {1}{4}}}{\sqrt {\textit {\_a}}}d \textit {\_a} \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.426 (sec). Leaf size: 133
DSolve[y'[x] + 2*(a^2*x^3 - b^2*x)*y[x]^3 + 3*b*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [c_1=\sqrt [4]{\left (\frac {b}{a x}-\frac {1}{a x^2 y(x)}\right )^2-1} \left (-\frac {\left (\frac {b}{a x}-\frac {1}{a x^2 y(x)}\right ) \, _2F_1\left (\frac {1}{2},\frac {3}{4};\frac {3}{2};\left (\frac {b}{a x}-\frac {1}{a x^2 y(x)}\right )^2\right )}{2 \sqrt [4]{1-\left (\frac {b}{a x}-\frac {1}{a x^2 y(x)}\right )^2}}-\frac {a x}{b}\right ),y(x)\right ] \]