# Engineering Mathematics Solved Problems

(a) dx dt −kx= 0 (b) d 3 x dt 3 t 2 dx dt =t d dt (xt) (d) d dt t d dt (t 2 x) =xt.(3) Determine which members of the given sets are solutions of the differential equation.

(a) dx dt −kx= 0 (b) d 3 x dt 3 t 2 dx dt =t d dt (xt) (d) d dt t d dt (t 2 x) =xt.(3) Determine which members of the given sets are solutions of the differential equation.(1) Which of the following sets are linearly independent and which are linearly dependent?

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(c) Calculate the inverse Laplace transform of I 2 (s).

[8] (d)Calculatei 1 (t) by insertingi 2 (t) and its derivative into the original equation.

If you are having difficulties with these questions practice using the remaining questions from these exercise.

[20] SCEE08009 Engineering Mathematics 2A Tutorial 2 (d) ( d 3 x dt 3 t d 2 x dt 2 x 2 t= sint, x(1) = 1,x ̇(1) = 0,x ̈(1) =− 2. 2 ,x ̇(1) = 1,x ̈(1) = 0, using forward Euler with a step size of ∆t= 0.025s.

Repeat the calculation with ∆t= 0.0125 and hence estimate the accuracy of your solution att= 2.

The analytical solution to this BVP is x=e 3 t 2 (28π 3 35π) sint 320 π 4 800π 2 3380 21 πcost 80 π 4 200π 2 845 (28π 2 −91) sinπt− 84 πcosπt 320 π 4 800π 2 3380 Calculate the predicted position,x 50 , which is found by performing 50 time steps with the forward Euler ODE solver with a uniform time step, ∆t= 0.1s.

By comparing x 50 with the analytical solution,x(5), comment on the accuracy of your solution.

## Comments Engineering Mathematics Solved Problems

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