Solution to the differential equation $$x+x33$$!$$+x55$$!$$+$$...$$.1+x22$$!$$+x44$$!....$$=dx$$−$$dydx+dy$$

Correct option is 22y e2x=c e2x−1

Questions

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

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2y e2x=c e2x+1

2y e2x=c e2x−1

2y e2x=c e2x+2

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detailed solution

Correct option is B

Given equation can be written assinhxcoshx=1−dydx1+dydxApply componendo and dividendosinh⁡x+cosh⁡xsinh⁡x−cosh⁡x=2−2dydx⇒ex−e−x=dx-dy⇒dy=e−2xdxIntegrate we gety=e−2x−2+c2⇒−2ye2x=1−ce2x⇒2ye2x=ce2x−1

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Solution to the differential equation x+x33!+x55!+....1+x22!+x44!....=dx−dydx+dy

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