Solve the initial–value problem

MATHEMATICS · Single correct · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

Solve the initial–value problem dydx=(1+y2)ex,y(0)=0\dfrac{dy}{dx}=(1+y^{2})e^{x},\quad y(0)=0. Which of the following gives yy as an explicit function of xx? (a) y=tan⁡(ex)y=\tan(e^{x}) (b) y=tan⁡(ex−1)y=\tan(e^{x}-1) (c) y=arctan⁡(ex−1)y=\arctan(e^{x}-1) (d) y=tan⁡(ex)−tan⁡1y=\tan(e^{x})-\tan 1

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