Internal problem ID [8482]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 146.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
\[ \boxed {x^{2} y^{\prime }+y^{3} x +a y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 65
dsolve(x^2*diff(y(x),x) + x*y(x)^3 + a*y(x)^2=0,y(x), singsol=all)
\[ c_{1} +{\mathrm e}^{-\frac {\left (\left (-x +a \right ) y \left (x \right )+x \right ) \left (\left (a +x \right ) y \left (x \right )+x \right )}{2 y \left (x \right )^{2} x^{2}}} x +\frac {\operatorname {erf}\left (\frac {\sqrt {2}\, \left (a y \left (x \right )+x \right )}{2 y \left (x \right ) x}\right ) \sqrt {2}\, \sqrt {\pi }\, a \,{\mathrm e}^{\frac {1}{2}}}{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.607 (sec). Leaf size: 78
DSolve[x^2*y'[x] + x*y[x]^3 + a*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {i a}{x}=\frac {2 e^{\frac {1}{2} \left (-\frac {i a}{x}-\frac {i}{y(x)}\right )^2}}{\sqrt {2 \pi } \text {erfi}\left (\frac {-\frac {i a}{x}-\frac {i}{y(x)}}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]