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If `y=y(x)`and `(2+sinx)/(y+1)((dy)/(dx))=-cosx ,y(0)=1,`then `y(pi/2)`equals(a)`( b ) (c) (d)1/( e )3( f ) (g) (h)`(i)(b) `( j ) (k) (l)2/( m )3( n ) (o) (p)`(q)(c) `( r ) (s)-( t )1/( u )3( v ) (w) (x)`(y) (d) 1A. `(1)/(3)`B. `(2)/(3)`C. `-(1)/(3)`D. 1 |
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Answer» Correct Answer - 1 We have `(2+sinx" dx")/(y+1" dx")=-cos x` int`("dy")/("y+1")=-int("cos x dx")/("2+sin x")` `log |y+1|=-log|2+sin x|+logC` `=log|(C)/("2+ sin x")|` `y+1=(C)/("2+ sin x")` Now `y+1(4)/("2+ sin x")` `"at x"=0,y=1, C=4` `"at x"=(pi)/(2)," "y=(1)/(2)` |
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