Internal problem ID [1977]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {{\mathrm e}^{x} y^{\prime }-2 x y^{2}-{\mathrm e}^{x} y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(exp(x)*diff(y(x),x)=2*x*y(x)^2+exp(x)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x}}{-x^{2}+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.286 (sec). Leaf size: 25
DSolve[Exp[x]*y'[x]==2*x*y[x]^2+Exp[x]*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^x}{x^2-c_1} \\ y(x)\to 0 \\ \end{align*}