Problem Description Find the solution of the following second order differential

Question

Problem Description Find the solution of the following second order differential equation: y"(t) 4 y' (t) 3 y(t) f(t) with initial conditions y(0) 1;y (0) 3 for the following values of f(t) 1) f(t 10 Once the solution is obtained, find the value of y() at timet 0.5. Return the solution to the ODE, i e.y(t) in the variable 'soln. Return the value of y(0.5) upto 6 significant places and store itin the variable 'valPrecision. Use the Symbolic Math Toolbox functions for this question. In particular, consider using "dsolve" to solve differential equations and "vpa" to perform variable precision arithmetic. Solution EA MATLAB Documentation 1 function [soun,valPrecision] your fcn name 3 Hint: Use the subs" function when calculating y (0.5) 5 clc 7 Declare y(t) as a symbolic function. Also define its derivatives 8 syms y(t) 9 Dy diff (y) 10 't' is the independent variable ll syms t 12 13 v Do not change the code above this comment.

Explanation / Answer

function [soln,valPrecision] = your_fcn_name

   clc;
   syms y(t);
   Dy = diff(y);
  
   syms t;
  
   eqn = diff(y,t,2) == 4*Dy - 3*y + 10;
   cond1 = y(0) == 1;
   cond2 = Dy(0) == -3;
  
   conds = [cond1 cond2];
   soln = dsolve(eqn,conds);
   soln = simplify(ySol);
  
   t = 0.5;
   val = subs(y);
   valPrecision = vpa(val,6);

end

[func,val] = your_fcn_name

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