Internal problem ID [3990]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli
Equations
Problem number: Exercise 11.4, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x^{\prime }+2 y x-{\mathrm e}^{-y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 14
dsolve(diff(x(y),y)+2*y*x(y)=exp(-y^2),x(y), singsol=all)
\[ x \relax (y ) = \left (y +c_{1}\right ) {\mathrm e}^{-y^{2}} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 17
DSolve[x'[y]+2*y*x[y]==Exp[-y^2],x[y],y,IncludeSingularSolutions -> True]
\begin{align*} x(y)\to e^{-y^2} (y+c_1) \\ \end{align*}