38.1.2 problem 2

Internal problem ID [6419]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Test excercise 24. page 1067
Problem number : 2
Date solved : Monday, January 27, 2025 at 02:01:07 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

\[ y = \tan \left (\frac {-1+c_1 \left (x +1\right )}{x +1}\right ) \]

✓ Solution by Mathematica

Time used: 0.301 (sec). Leaf size: 32

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

\begin{align*} y(x)\to -\tan \left (\frac {1}{x+1}-c_1\right ) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}