Can someone help me "Error using sym/diff"

Can someone help me with this please!

My question :

and I stuck here:

Thank you so much !!

Answer 1

[Dyuman Joshi]

1) Your approach of declaring syms variable and taking x from -pi to pi as initial condition for using dsolve is incorrect .

2) Since, your question asks to verify (meaning you don't need to solve the equation) numerically, you can do something like this.

syms x y
y = sin(x) + 2*cos(x);
z = diff(y,2) + y

z = 

0

As you can see that, the value of differential equation is 0 for any value of x.

Answer 2

[Walter Roberson]

Your approach is wrong for the question. It asks for numeric verification.

So take x = linspace() a range notably wider than [-pi, pi] because you need several periods in order to verify periodic behaviour.

Then evaluate y = sin(x) + 2*cos(x) for that numeric x.

Now, do numeric differentiation,

dy = gradient(x, y);
d2y = gradient(x, dy);

and compare d2y + dy to 0