Internal problem ID [4535]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12,
Miscellaneous Methods
Problem number: Exercise 12.14, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {x y^{\prime }+y-x^{2} \left ({\mathrm e}^{x}+1\right ) y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x*diff(y(x),x)+y(x)=x^2*(1+exp(x))*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{\left (x +{\mathrm e}^{x}-c_{1} \right ) x} \]
✓ Solution by Mathematica
Time used: 0.249 (sec). Leaf size: 55
DSolve[x*y'[x]+y[x]==x^2*(1+exp[x])*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-x \int _1^x(\exp (K[1])+1)dK[1]+c_1 x} y(x)\to 0 y(x)\to -\frac {1}{x \int _1^x(\exp (K[1])+1)dK[1]} \end{align*}