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Let y = y(x) be the solution of the differential equation $\frac{d y}{d x} = 2 (y + 2 s i n x - 5) x - 2 c o s x$ such that that y(0) = 7. Then y(p) is equal to

Option 1 -

$7 e^{π^{2}} + 5$

Option 2 -

$2 e^{π^{2}} + 5$

Option 3 -

$3 e^{π^{2}} + 5$

Option 4 -

$e^{π^{2}} + 5$

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

$\frac{d y}{d x} = 2 (y + 2 s i n x - 5) x - 2 c o s x$

where P = -2x, Q = 4x sin x – 10x – 2 cosx

Solution be $y . e^{- x^{2}} = \int (4 x s i n x - 10 x - 2 c o s x) . e^{- x^{2}} d x + c$

$y . e^{- x^{2}} \int (4 x s i n x - 10 x - 2 c o s x) . e^{- x^{2}} d x + c$

$y . e^{- x^{2}} = e^{- x^{2}} (5 - 2 s i n x) + c . . . . . . . . (i)$

Put x = 0, y = 7 then 7 = 5 + c i.e. c = 2

Put x = p then $y . e^{- π^{2}} = 5 . e^{- π^{2}} + 2$

y = 5 + $2 e^{x^{2}}$

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Let y = y(x) be the solution of the differential equation $\frac{d y}{d x} = 2 (y + 2 s i n x - 5) x - 2 c o s x$ such that that y(0) = 7. Then y(p) is equal to

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Let y = y(x) be the solution of the differential equation d y d x = 2 ( y + 2 s i n x − 5 ) x − 2 c o s x such that that y(0) = 7. Then y(p) is equal to

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Let y = y(x) be the solution of the differential equation $\frac{d y}{d x} = 2 (y + 2 s i n x - 5) x - 2 c o s x$ such that that y(0) = 7. Then y(p) is equal to