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Q1nbsp find a general solution of the following ordinary

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Reference no: EM13375652

Q.1  Find a general solution of the following ordinary differential equations:

 (a) y' = 3(y+1)         (b) y' = y2sinx       (c) y' = e2xcos2y.

Q.2  Solve the following  differential equations with the given initial values.

 (a) y' = x3e-y ,      y(2) = 0

(b)   y'cosh2x + sinh2y =0 , y(0) = -2

Plot the solutions.

3. (a)  Solve the following differential equation with the given initial value ( initial value problem:

           y' = y/x + 2x3cosx2/y    ;       y(√Π) = 0   . Plot the solution.

        b) Find the general solution of the following ordinary differential equation.

            x2y' = y2+xy

Q.4  (a) Solve the following initial value problem:

                 y' + ytanx = sin2x,  y(0) = 1

         (b) Find the general solutions of the following differential equation:

                         xy' + 2y = 9x

Q.5   Solve the following initial value problems:

                 (a)  y' + 3y = 12, y(0) = 6

Plot the solution of (a).

                 (b) y' + ky, e-kx , y(0) = 0.7

Q.6 Find a general solution of the following system of linear differential equations:

             y1' = y1 + y2    .

            y2' = 3y1 - y2

Q.7 Find a general solution of the following system of linear differential equations:

            y1' = y1 - y2   

             y2' = y1 + y2.

Q.8 Find a general solution of the following system:

y1" = 3y1 -y2 + 2y3

y2' = -4y2 + 2y3

y3' = y2 -5y3  

Reference no: EM13375652

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