32.6.14 problem Exercise 12.14, page 103

Internal problem ID [5879]
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
Date solved : Monday, January 27, 2025 at 01:23:34 PM
CAS classification : [_Bernoulli]

\begin{align*} x y^{\prime }+y&=x^{2} \left (1+{\mathrm e}^{x}\right ) y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (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: 0.272 (sec). Leaf size: 55

DSolve[x*D[y[x],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*}