7.3.20 problem 20

Internal problem ID [60]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 20
Date solved : Friday, February 07, 2025 at 07:47:22 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: 0.029 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.195 (sec). Leaf size: 15

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

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