8.3.19 problem 20

Internal problem ID [695]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 20
Date solved : Wednesday, February 05, 2025 at 03:51:15 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 12

dsolve([diff(y(x),x) = 3*x^2*(1+y(x)^2),y(0) = 1],y(x), singsol=all)
 

\[ y = \tan \left (x^{3}+\frac {\pi }{4}\right ) \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 15

DSolve[{D[y[x],x]== 3*x^2*(1+y[x]^2),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \tan \left (x^3+\frac {\pi }{4}\right ) \]