8.2.15 problem 19

Internal problem ID [675]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 19
Date solved : Monday, January 27, 2025 at 02:57:27 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

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

\[ y(x)\to 0 \]