71.3.15 problem 10

Internal problem ID [14365]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 06:27:48 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=1+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 8

dsolve(diff(y(x),x)=1+y(x)^2,y(x), singsol=all)
 

\[ y = \tan \left (x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 41

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+1}dK[1]\&\right ][x+c_1] \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}