47.1.9 problem 9

Internal problem ID [7390]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 9
Date solved : Monday, January 27, 2025 at 02:51:47 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 9

dsolve([x*diff(y(x),x)+y(x)=y(x)^2,y(1) = 1/2],y(x), singsol=all)
 

\[ y = \frac {1}{x +1} \]

✓ Solution by Mathematica

Time used: 0.258 (sec). Leaf size: 10

DSolve[{x*D[y[x],x]+y[x]==y[x]^2,{y[1]==1/2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{x+1} \]