Chapter 9, Problem 1P

To determine

To write:

A MATLAB code that finds the solution of the equation $e^{0.3x}-x^2=-4$.

Answer to Problem 1P

Solution:

The solution of the equation $e^{0.3x}-x^2=-4$ is $x_1=2.4693$.

Explanation of Solution

The given equation is, $f\left(x\right)=e^{0.3x}-x^2+4$

Plot the graph of the above equation.

Figure (1)

The solution of the above equation is $x_1=2.4693$.

Write the MATLAB code that finds the solution of the equation $e^{0.3x}-x^2=-4$.

MATLAB Code:

fplot('exp(0.3*x)-x^2+4',[0 5])

xlabel('x<<')

ylabel('y<<')

% Plot of the function shows that the function has one solution between 2 and 4

F = @ (x) exp(0.3*x)-x^2+4;

x1 = fzero(F,2.5)

Save the MATLAB script with the name, Chapter9_29864_9_1P.m in the current folder. Execute the script by typing the script name at the command window to get the code that finds the solution of the equation $e^{0.3x}-x^2=-4$.

Result:

Conclusion:

Therefore, the solution of the equation $e^{0.3x}-x^2=-4$ is $x_1=2.4693$.