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+1 vote
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in Differential Equations by (28.9k points)
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(i) The general solution of the DE \(\frac{dy}{dx}\) =ex−y is 

(a) ey + ex = c

(b) ey ex = c

(c) e-y + e-x = c

(d) ey – ex = c

(ii) Solve the DE \(\frac{dy}{dx} = \frac{2xy}{1+x^2}+x^2+2\)

1 Answer

+1 vote
by (28.2k points)
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Best answer

(i) (d) ey – ex = c

(ii)

⇒ \(\frac{y}{1 + x^2} = x + tan ^{-1} + c\)

⇒ y = (1 + x2)(x + tan-1 + c)

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