Differential Eqs 2

Differential Eqs 2 - A , g , h and k are constants Solve...

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205FOE102 Further Mathematics 1 Differential Equations 2 Linear Equations 1. Find the general solutions of the differential equations. (a) 7 5 x y dx dy x = - (b) x e y dx dy 4 2 = + (c) x y x dx dy 2 1 - + = (d) x x y dx dy x 3 cos sin 2 cos = + (e) ( 29 1 2 1 2 = - + x x y dx dy (f) x x y dx dy cos cot = - 2. Solve the following initial value problems. (a) 3 2 2 + = - t te x dt dx , ( 29 0 0 = x (b) ( 29 ( 29 3 2 2 - = - - t x dt dx t , ( 29 10 4 = x (c) t e t x dt dx 2 5 - = - + , ( 29 75 72 0 = x 3. The following simple model can represent the unsteady flow of water through a hydroelectric power generation system when a control valve setting is changed. gh kQ dt dQ A d ρ = + where Q is the volume flow rate at time t , d ,
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Unformatted text preview: A , g , h and k are constants Solve this equation to obtain an expression for the volume flow rate as a function of time. Initially, the volume flow rate is Q . Miscellaneous 4. Use an appropriate method to find the general solutions of the following differential equations. (a) x x y dx dy x 2 2 + =-(b) ( 29 1 2 2 2 = + + xy dx dy x (c) x xe y dx dy-= + 3 (d) ( 29 4 =-+ dx dy x x y (e) ( 29 ( 29 ( 29 3 4 2 3 1 + = + + + x x y x dx dy x x...
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