32.6.21 problem Exercise 12.21, page 103

Internal problem ID [5886]
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 12.21, page 103
Date solved : Monday, January 27, 2025 at 01:24:36 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }-y^{2}+1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 11

dsolve(x*diff(y(x),x)-y(x)^2+1=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.520 (sec). Leaf size: 43

DSolve[x*D[y[x],x]-y[x]^2+1==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1-e^{2 c_1} x^2}{1+e^{2 c_1} x^2} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}