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1. (ii) [ 5 Marks ] Solve non-homogenous differential bustion dy x + y equati dx...
solve the differential equation dy y(x - y) dx x2
Solve the differential equation dx ex dy y 2 x Il
If S= {e*, e*, xe* is a fundamental solution set for the homogenous differential equation with constant coefficients dy a2 dy +a dx2 d y + a y 0, dx dx find the values of a ,i= 0, 1, 2, 3 (5 markah/marks) Dengan nilai yang diperolehi dari (a), selesaikanlah masalah nilai awal yang berikut: (b) day 2 (1+2e) d2 y a a dx dy ax a ax dengan 0)1,y' (0)- 2,y (0)-3. By using the values obtained in (a),...
Solve the exact differential equation (4 x y tsin x) dx + (x" - Y) dy = 0
Question 2: solve the differential equations a) (xy - y)dx + - x)dy = 0
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt 7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
Solve the differential equation: (3- x?) y dy dx y +3/7–3
a) Consider the first-order differential equation (y + cos.r) dx + dy = 0. By multiplying integrating factor y(x) = ei" to both sides, show that the differential equation is exact. Hence, solve the differential equation. (6 marks) b) Solve the differential equation (4.r + 5)2 + ytan z = dc COSC (7 marks)
Solve the separable differential equation (y2+2)dx+y(x+4)dy=0.
5. Given the differential equation: dy 1 +-y = 3x2 dx Find (a) (b) the general solution for the differential equation; and (6 marks) the particular solution for the differential equation if the boundary condition is y(1) =2. (2 marks)