33.1.5 problem problem 146

Internal problem ID [6023]
Book : Differential Gleichungen, Kamke, 3rd ed, Abel ODEs
Section : Abel ODE with constant invariant
Problem number : problem 146
Date solved : Tuesday, January 28, 2025 at 03:10:10 PM
CAS classification : [_rational, _Abel]

\begin{align*} x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 65

dsolve(x^2*diff(y(x),x)+x*y(x)^3+a*y(x)^2 = 0,y(x), singsol=all)
 

\[ c_1 +{\mathrm e}^{-\frac {\left (\left (a +x \right ) y+x \right ) \left (\left (a -x \right ) y+x \right )}{2 y^{2} x^{2}}} x +\frac {\operatorname {erf}\left (\frac {\sqrt {2}\, \left (y a +x \right )}{2 y x}\right ) \sqrt {2}\, \sqrt {\pi }\, a \,{\mathrm e}^{\frac {1}{2}}}{2} = 0 \]

✓ Solution by Mathematica

Time used: 0.601 (sec). Leaf size: 78

DSolve[x^2*D[y[x],x]+x*y[x]^3+a*y[x]^2 == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {i a}{x}=\frac {2 e^{\frac {1}{2} \left (-\frac {i a}{x}-\frac {i}{y(x)}\right )^2}}{\sqrt {2 \pi } \text {erfi}\left (\frac {-\frac {i a}{x}-\frac {i}{y(x)}}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]