8.6.10 problem 10

Internal problem ID [780]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 10
Date solved : Wednesday, February 05, 2025 at 03:58:31 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

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

\[ y = \tan \left (\frac {1}{3} x^{3}+c_1 +x \right ) \]

✓ Solution by Mathematica

Time used: 0.188 (sec). Leaf size: 17

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

\[ y(x)\to \tan \left (\frac {x^3}{3}+x+c_1\right ) \]