76.1.34 problem 34

Internal problem ID [17333]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 34
Date solved : Tuesday, January 28, 2025 at 10:01:26 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.165 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.220 (sec). Leaf size: 11

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

\[ y(x)\to \tan (x (x+2)) \]