Local extreme values for a differential equation, using solve?

Question

Hassan 2013-5-2

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https://ww2.mathworks.cn/matlabcentral/answers/74372-local-extreme-values-for-a-differential-equation-using-solve

回答： Christopher Creutzig 2014-3-31

Hi,

I am trying to calculate the local extreme values for a differential equation using the function solve. The problem is the values I get does not match the extreme values I can see in the plot for the function.

This is the code:

 syms x y            %Symbolic x and y    
 f= (x^3*y+5*x^2*y)/(exp(x^2+3*y^4));   %The function
 figure(1)
 ezsurf(f,[-2,0.1,2],[-2,0.1,2])    %3D-plot
 grid on
 box on
 fx=diff(f,x)                        %Differeniate the function w.r.t x
 fy=diff(f,y)                        %Differeniate the function w.r.t y
 S=solve(fx,fy);                     %Solving the differential equations (=0)
 x = double(S.x);              %Rewrite the value to a number from the struct
 y = double(S.y);

If I run the code I get that x=0 and y=0, which cant not be correct compared to what is seen in the figure created in the code. I know that there are other methods to solve this problem, but this is the method I was told to use to solve this assignment.

Thank you for your help. Regards

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Answer 1

Christopher Creutzig 2014-3-31

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/74372-local-extreme-values-for-a-differential-equation-using-solve#answer_131467

I think they are correct, the solution is just not complete, since it was computed numerically.

You could try solve(simplify(fx), simplify(fy)) instead, which returns 18 solutions. If you restrict x and y to be real by calling syms x y real, you get 10 solutions.