Internal problem ID [3342]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 78.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Abel]
\[ \boxed {y^{\prime }-\left (a \,{\mathrm e}^{x}+y\right ) y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 62
dsolve(diff(y(x),x) = (a*exp(x)+y(x))*y(x)^2,y(x), singsol=all)
\[ \frac {a \,\operatorname {erf}\left (\frac {\left (a \,{\mathrm e}^{x} y \left (x \right )+1\right ) \sqrt {2}}{2 y \left (x \right )}\right ) \sqrt {2}\, \sqrt {\pi }+2 c_{1} a +2 \,{\mathrm e}^{-x -\frac {\left (a \,{\mathrm e}^{x} y \left (x \right )+1\right )^{2}}{2 y \left (x \right )^{2}}}}{2 a} = 0 \]
✓ Solution by Mathematica
Time used: 0.702 (sec). Leaf size: 78
DSolve[y'[x]==(a Exp[x]+y[x])y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-i a e^x=\frac {2 e^{\frac {1}{2} \left (-i a e^x-\frac {i}{y(x)}\right )^2}}{\sqrt {2 \pi } \text {erfi}\left (\frac {-i a e^x-\frac {i}{y(x)}}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]