# (a) dy/dx-1+y^2

Question
Integrals
(a) $$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}-{1}+{y}^{{2}}$$

2020-10-29
Given Differential equations is $$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={1}+{y}^{{2}}$$ with y(0)=0. Now PSKdy/dx=1+y^2 -> dy/(1+y^2)=dx ->∫(dy/1+y^2)=∫dx+CZSK, where C is a integrating constant $$\displaystyle\to{\arctan{{y}}}={x}+{C}$$ Now, $$\displaystyle{y}{\left({0}\right)}={\left({0}\right)}\to{C}={0}$$ Hence, the solution is arctany=x->y=tanx

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