Solve a second order differential equation with ODE45, RK4 and draw with power series

Hi, I am completely new to Matlab and am looking to solve a simple second order differential equation:

y''+x*y=0, −∞ < x < ∞.

I am looking to solve for y(x) with rk4, ode45

And plotting with power series these general solutions.

I understand this is a simple equation to solve and have done it fine on paper. However I have been trying different ways to solve it on matlab but to no avail.

Thanks in advance

[Jan]

Do you want a numerical solution for a certain initial value or a symbolic solution?

[jaehyeong park]

symbolic solution

Answer 1

[Jyotsna Talluri]

Second order differential equations can be slved using 'dsolve'

syms y(x)
Dy = diff(y);
eqn = diff(y,x,2) == -x*y;
y(x) = dsolve(eqn);
y = simplify(y);

Refer to the dsolve for more information

Answer 2

[JONNALA SISINDRA REDDY]

syms y(x)

Dy = diff(y);

eqn = diff(y,x,2) == -x*y;

y(x) = dsolve(eqn);

y = simplify(y);