60.1.111 problem 111

Internal problem ID [10125]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 111
Date solved : Tuesday, January 28, 2025 at 04:25:46 PM
CAS classification : [_rational, _Abel]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 57

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

\[ \frac {3 \,\operatorname {erf}\left (\frac {i \left (3 x y-1\right ) \sqrt {2}}{2 y}\right ) \sqrt {2}\, \sqrt {\pi }\, x -2 i {\mathrm e}^{\frac {\left (3 x y-1\right )^{2}}{2 y^{2}}}+6 c_{1} x}{6 x} = 0 \]

✓ Solution by Mathematica

Time used: 0.327 (sec). Leaf size: 55

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

\[ \text {Solve}\left [-3 x=\frac {2 e^{\frac {1}{2} \left (\frac {1}{y(x)}-3 x\right )^2}}{\sqrt {2 \pi } \text {erfi}\left (\frac {\frac {1}{y(x)}-3 x}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]