[Solved] Given the MATLAB code:f = @(t,y) t + y; [t,y] = ode45(f, [0 1], 1); disp(y(end));What is the approximate value displayed? | MATLAB

MATLAB - Numerical Methods

Given the MATLAB code:

f = @(t,y) t + y;
[t,y] = ode45(f, [0 1], 1);
disp(y(end));

What is the approximate value displayed?

A0.5

B1.0

C2.7

D3.5

Step-by-Step Solution

Solution:

Step 1: Understand the ODE
The equation is dy/dt = t + y with y(0)=1.
Step 2: Recognize the solution behavior
This is a linear ODE with increasing solution; the exact solution at t=1 is about 2.718 (e - 1 + 1).
Step 3: Check code output
ode45 numerically approximates this, so y(end) is close to 2.7.
Final Answer:
2.7 -> Option C
Quick Check:
Value near e (2.718) expected [OK]

Quick Trick: dy/dt = t + y grows near e at t=1 [OK]

Common Mistakes:

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