(a) Use the method of direct Integration to find the solution of x2. (b) (i) dy...

 

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(a) Use the method of direct Integration to find the solution of x2. (b) (i) dy -4x=6. (5%) dx Verify that y = ex, y = e3x and y = Aex + Be -3x (A and B are constants) are - 6y= 0. (10 %) solutions to the differential equation dy dy + dx dx (ii) Comment on the relation between y, y and y3. (3%) (c) Determine the order of the following differential equations, and state if they are linear or non-linear in nature: 2 (i) (d2y 4 + dx + 4y = cos x dx dt dx - e sin t dt = e-t (ii) at dy (iii) + cos y=x dx dy dy (iv) dx4 +y = dx 0 (2%) (2%) (2%) (2%) (a) Use the method of direct Integration to find the solution of x2. (b) (i) dy -4x=6. (5%) dx Verify that y = ex, y = e3x and y = Aex + Be -3x (A and B are constants) are - 6y= 0. (10 %) solutions to the differential equation dy dy + dx dx (ii) Comment on the relation between y, y and y3. (3%) (c) Determine the order of the following differential equations, and state if they are linear or non-linear in nature: 2 (i) (d2y 4 + dx + 4y = cos x dx dt dx - e sin t dt = e-t (ii) at dy (iii) + cos y=x dx dy dy (iv) dx4 +y = dx 0 (2%) (2%) (2%) (2%)