(a) If x=e, show that xDy=and x'D'y-d Hence, or otherwise, solve the equation 'D'y-3xDy+5y=3x+ In.x. Solve...

    

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(a) If x=e, show that xDy=and x'D'y-d Hence, or otherwise, solve the equation 'D'y-3xDy+5y=3x+ In.x. Solve the following differential equations: (b) (i) +y=r. (i) d-3x dy -3x+4y=6x In.x+ dx dx d'y dy dy (iv) +2x-2y= x+3x dx' dx dx (c) If r sin x and y = y(x), dy d'y dy (i) Prove that dx di cos x-sinx. dt d'y (ii) dy (ii) -3y=x' Inx dx Transform the differential equation +tan x+ycosx=2e** cos*x dy dx into an equation connecting y and r when t=sin.x. Hence, Solve the equation. (a) If x=e, show that xDy=and x'D'y-d Hence, or otherwise, solve the equation 'D'y-3xDy+5y=3x+ In.x. Solve the following differential equations: (b) (i) +y=r. (i) d-3x dy -3x+4y=6x In.x+ dx dx d'y dy dy (iv) +2x-2y= x+3x dx' dx dx (c) If r sin x and y = y(x), dy d'y dy (i) Prove that dx di cos x-sinx. dt d'y (ii) dy (ii) -3y=x' Inx dx Transform the differential equation +tan x+ycosx=2e** cos*x dy dx into an equation connecting y and r when t=sin.x. Hence, Solve the equation.