Internal problem ID [4568]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x +1\right )^{2} y^{\prime }-1-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve((1+x)^2*diff(y(x),x)=1+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\frac {c_{1} x +c_{1}-1}{x +1}\right ) \]
✓ Solution by Mathematica
Time used: 0.52 (sec). Leaf size: 32
DSolve[(1+x)^2*y'[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*}