solve the symbolic function y(x)=f(x)*(c1*x+c2)+g(x), choosing c1 and c2, so y(0) and y(l) = 0 in matlab

To solve the symbolic function y(x) = f(x)(c1x+c2) + g(x), where c1 and c2 are constants, and to satisfy the conditions y(0) = 0 and y(l) = 0 in MATLAB, you can follow these steps:

1. Define the symbolic variables and constants:

main.m
syms x c1 c2 % Define symbolic variables
l = 1; % Define the value of l
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2. Define the symbolic function y(x):

main.m
y(x) = f(x)*(c1*x + c2) + g(x);
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3. Set up the equations y(0) = 0 and y(l) = 0:

main.m
eqn1 = y(0) == 0;
eqn2 = y(l) == 0;
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4. Solve the equations symbolically for c1 and c2:

main.m
sol = solve([eqn1, eqn2], [c1, c2]);
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5. Access the values of c1 and c2 in the solution:

main.m
c1_sol = sol.c1;
c2_sol = sol.c2;
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Now you have the values of c1 and c2 that satisfy the conditions y(0) = 0 and y(l) = 0 in the symbolic function y(x).