60.1.37 problem 37

Internal problem ID [10051]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 37
Date solved : Tuesday, January 28, 2025 at 04:15:29 PM
CAS classification : [_Abel]

\begin{align*} y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 62

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

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

✓ Solution by Mathematica

Time used: 0.685 (sec). Leaf size: 78

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

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