Consider the differential equation

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

Problem

Consider the differential equation dydx=xey\dfrac{dy}{dx}=x e^{y}. Which of the following gives the explicit general solution y(x)y(x)? (a) y=−ln⁡ ⁣(x22+C)y = -\ln\!\left(\dfrac{x^{2}}{2}+C\right) (b) y=−ln⁡ ⁣(−x22+C)y = -\ln\!\left(-\dfrac{x^{2}}{2}+C\right) (c) y=ln⁡ ⁣(−x22+C)y = \ln\!\left(-\dfrac{x^{2}}{2}+C\right) (d) y=ln⁡ ⁣(x22+C)y = \ln\!\left(\dfrac{x^{2}}{2}+C\right)

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