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S. 2004) 1:. sin 2x = sin x cos x 2 :. Integrating factor = e fPdx = efcos x dx = e sin x Multiplying the given equation by the integrating factor esin with respect to x, we get 18 x and integrating Differential Equations of First Order and First Degree y. e sin x = C + JeSin x sin x cos x dx, where C is an arbitrary constant. y. e sin x = C + Jet t dt, or = C + t. e t = C + esinx (sin x -1) where t = sin x et - y. e sin x = C + esin x (sin x - 1) or Equations Reducible to the Linear Form. The equation (1) Where P and Q are constants or functions of x alone and n is a constant other than zero or unity is called the extended form of linear equation or Bernoulli's Equation.

B) 14. S. 1994) (a) y+ x = a tan (y : c) c) y (c) y - x = tan ( -a- (b) (y - x) = a tan (y - c) (d) y a (y - x) = tan ( -a- -c) Ans. (a) 36 Differential Equations of First Order and First Degree 15. 1994) (a) sin y + cos y (c) x2 -cosy (b) - siny (d) cosy Ans. (c) 16. S. 1993) y2 (a) ye Ix (c) ye x/y2 A (b) = A (d) = 17. 1994) (a) y= ex 1 + eX 2 1 (c) y= 1 + ce x2 (b) y= (d) y= 1 1- c eX ex 2 1 + eX Ans. (c) 18. 1996) . (a) y = vx (c) x + Y =v (b) xy=v (d) x-y=v Ans. (a) 19. The solution of the differential equation dy + y...

D) 3. CS. 1999) (a) 2x (y')2 + 1 = 2yy' (b) 2xy + 1 = 2yy' (c) 2x2y' + 1 = 2yy' (d) 2 (y')2 + x = 2yy' Ans. (a) 4. 2oo0) (a) xy = C eX-Y (b) x+y=Ce xy (c) xy = C eY-X (d) x-y=Ce xy Ans. (c) 34 Diiferential Equations of First Order and First 5. 2000) (a) 1 + x2 (b) (c) log (1 + X2) (d) -log (1 + x2) Ans. (a) 6. 2oo0) (a) (e6 + 9)/2 (b) (c) log e6 (d) Ans. (a) 7. The solution of (x -1) dy = Y dx, Y (0) = -5 is (a) y = 5 (x -1) (b) Y = -5 (x - 1) (c) Y = 5 (x + 1) Ans. (a) (d) Y = -5 (x + 1) 8. S.