10.2.26 problem 26

Internal problem ID [1154]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 26
Date solved : Monday, January 27, 2025 at 04:37:02 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: 0.041 (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: 0.211 (sec). Leaf size: 11

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

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