Solution to the differential equation x-x3-3 -x5-5 -1-x2-2 -x4-4 - - - -d x-d y-d x-d yisA- 2 y - e2 x-C - e2 x-1B- 2 y - e2 x-C - e2 x-1C- y - e2 x-C - e2 x-2D- 2 x - e 2 y - C - e x -1

The correct option is B 2y.e^2x=C.e^2x 1 Applying C and D,we get dy/dx=e^ x/e^x=e^ 2x 2y= e^ 2x+c ...

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Variable Separable Method

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Solution to the differential equation $\frac{x + \frac{x^{3}}{3!} + \frac{x^{5}}{5!} + \dots \dots}{1 + \frac{x^{2}}{2!} + \frac{x^{4}}{4!} + \dots \dots} = \frac{d x - d y}{d x + d y}$ is

$2 y . e^{2 x} = C . e^{2 x} + 1$

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$2 y . e^{2 x} = C . e^{2 x} - 1$

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$y . e^{2 x} = C . e^{2 x} + 2$

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$2 x . e^{2 y} = C . e^{x} - 1$

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\frac{x + \frac{x^{3}}{3!} + \frac{x^{5}}{5!} + . . . . . . .}{1 + \frac{x^{2}}{2} + \frac{x^{4}}{4!} + . . . . . .} = \frac{d x - d y}{d x + d y}

\frac{x + \frac{x^{3}}{3!} + \frac{x^{5}}{5!} + . . . . .}{1 + \frac{x^{2}}{2!} + \frac{x^{4}}{4!} + . . . . .} = \frac{d x - d y}{d x + d y}

\frac{x + \frac{x^{3}}{3!} + \frac{x^{5}}{5!} + . . . . .}{1 + \frac{x^{2}}{2!} + \frac{x^{4}}{4!} + . . . . .} = \frac{d x - d y}{d x + d y}

y = 1 + x - \frac{x^{2}}{2!} - \frac{x^{3}}{3!} + \frac{x^{4}}{4!} + \frac{x^{5}}{5!} - . . . . . . . .

\frac{d y}{d x} =

The solution of the differential equation $x \frac{d y}{d x} + y = x^{2} + 3 x + 2$ is

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