Equation plot problem of dy/dx

Question

buer 2015-11-24

2
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https://ww2.mathworks.cn/matlabcentral/answers/257206-equation-plot-problem-of-dy-dx

回答： Star Strider 2015-11-24

Hi,

I have one problem does not understand. I have an equation for example: Z=A*dB/dt + B*dA/dt . I know A and B, but how can I plot Z? how I can express dA/dt or dB/dt? I tried with diff(A)./diff(t) this give 1 elements less than A. so it make B*dA/dt not possible. can anyone help.

Thanks a lot.

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Answer 1

Star Strider 2015-11-24

1
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The gradient function will calculate the first derivative, giving a result the same length as the input vector.

For example:

t = linspace(0, 1);
A = exp(-5*t) .* sin(6*pi*t);                           % Create Function ‘A’
B = cos(exp(-2*t)*2*pi);                                % Create Function ‘B’
dAdt = gradient(A,t);
dBdt = gradient(B,t);
Z = A.*dBdt + B.*dAdt;
figure(1)
plot(t, Z)
grid
xlabel('t')
ylabel('Z')

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Answer 2

Walter Roberson 2015-11-24

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Z=A*dB/dt + B*dA/dt needs to be understood in terms of symbolic A and B,

Z = A(t) * diff(B(t),t) + B(t) * diff(A(t),t)

with A(t) and B(t) functions, this is of course the same as

Z = diff( A(t) .* B(t), t)

As they are functions, you need to substitute the formulas for the functions into Z. Then you evaluate the resulting formula over the set of t values that you want to plot at.