67.1.2 problem Problem 1(b)

Internal problem ID [13949]
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(b)
Date solved : Tuesday, January 28, 2025 at 06:09:25 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.229 (sec). Leaf size: 30

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

\begin{align*} y(x)\to \tan \left (\frac {-1+c_1 x}{x}\right ) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}