Internal problem ID [7623]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 42.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Abel]
Solve \begin {gather*} \boxed {y^{\prime }-x \left (x +2\right ) y^{3}-\left (x +3\right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 40
dsolve(diff(y(x),x) - x*(x+2)*y(x)^3 - (x+3)*y(x)^2=0,y(x), singsol=all)
\[ c_{1}+\arctanh \left (\frac {\sqrt {y \relax (x )}\, x}{\sqrt {x \left (x +2\right ) y \relax (x )+2}}\right )+\frac {\sqrt {x \left (x +2\right ) y \relax (x )+2}}{2 \sqrt {y \relax (x )}} = 0 \]
✓ Solution by Mathematica
Time used: 0.73 (sec). Leaf size: 485
DSolve[y'[x] - x*(x+2)*y[x]^3 - (x+3)*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [c_1=-\frac {\frac {i \sqrt {\frac {2}{\pi }} \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}} \left (\frac {\sinh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}-\cosh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}-\frac {i \sqrt {\frac {2}{\pi }} \left (\frac {x+1}{2}+\frac {1}{2}\right ) \sinh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}}{\frac {i \sqrt {\frac {2}{\pi }} \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}} \left (i \sinh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )-\frac {i \cosh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}-\frac {\sqrt {\frac {2}{\pi }} \left (\frac {x+1}{2}+\frac {1}{2}\right ) \cosh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}},y(x)\right ] \]