67.1.6 problem Problem 1(f)

Internal problem ID [13953]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 2, First Order Equations. Problems page 149
Problem number : Problem 1(f)
Date solved : Tuesday, January 28, 2025 at 06:09:34 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+y&=x y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(x*diff(y(x),x)+y(x)=x*y(x)^2,y(x), singsol=all)
 

\[ y = \frac {1}{\left (-\ln \left (x \right )+c_{1} \right ) x} \]

✓ Solution by Mathematica

Time used: 0.137 (sec). Leaf size: 22

DSolve[x*D[y[x],x]+y[x]==x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{-x \log (x)+c_1 x} \\ y(x)\to 0 \\ \end{align*}