The general solution of frac{dy}{dx} = 2xye^{ | vedclass

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(C) Given the differential equation: $\frac{dy}{dx} = 2xye^{x^2}$.Separate the variables $x$ and $y$:$\frac{dy}{y} = 2x e^{x^2} dx$.Integrate both sid

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$y = c e^{e^{x^2}}$

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(C) Given the differential equation: $\frac{dy}{dx} = 2xye^{x^2}$.Separate the variables $x$ and $y$:$\frac{dy}{y} = 2x e^{x^2} dx$.Integrate both sides:$\int \frac{dy}{y} = \int 2x e^{x^2} dx$.Let $u = x^2$,then $du = 2x dx$.The integral becomes:$\ln|y| = \int e^u du = e^u + C = e^{x^2} + C$.Exponentiating both sides:$|y| = e^{e^{x^2} + C} = e^C \cdot e^{e^{x^2}}$.Let $c = \pm e^C$,then the general solution is:$y = c e^{e^{x^2}}$.

The general solution of $\frac{dy}{dx} = 2xye^{x^2}$ is

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