8.3.17 problem 18

Internal problem ID [693]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 18
Date solved : Wednesday, February 05, 2025 at 03:51:12 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

\[ y = -\tan \left (\frac {c_1 x +x^{2}+1}{x}\right ) \]

✓ Solution by Mathematica

Time used: 0.286 (sec). Leaf size: 17

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

\[ y(x)\to -\tan \left (x+\frac {1}{x}-c_1\right ) \]