Question

1) Write an algorithm (i.e. the series of steps) to find the solution to a second order non-homogenous ODE (with boundary conditions) using the method of undetermined coefficients. (Note: this algorithm should include at least 1 control structure).
2) Write an if statement in MATLAB that converts an overall final percentage mark grade (1-7).

Answer 1

Answer:

1) General approach to solve IInd order non-homogeneous ODE using the method of undetermined constants can be described in the following steps:

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Let ODE be of the form:

ay''+by'+c = r(x)

where r(x) is finite linear combination of the form r(x) = r₁(x) + r₂(x) + --------------- + r_n(x)

If y_pi(x) is a solution to ay''+by'+c = r_i(x) then

y_p(x) = y_p1(x) + y_p2(x) + -----------------------+ y_pn(x) is a solution to ay''+by'+c = r(x)

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2) See the if statement below:

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if percentage >= 90
grade = 1;
elseif percentage >= 80 & percentage < 90
grade = 2;
elseif percentage >= 70 & percentage < 80
grade = 3;
elseif percentage >= 60 & percentage < 70
grade = 4;
elseif percentage >= 50 & percentage < 60
grade = 5;
elseif percentage >= 40 & percentage < 50
grade = 6;
else
grade = 7;
end

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