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

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jaehyeong park on 23 Nov 2019
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.
Jan on 23 Nov 2019
Do you want a numerical solution for a certain initial value or a symbolic solution?
jaehyeong park on 27 Nov 2019
Edited: jaehyeong park on 27 Nov 2019
symbolic solution

Jyotsna Talluri on 26 Nov 2019
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);

JONNALA SISINDRA REDDY on 7 Jun 2021
syms y(x)
Dy = diff(y);
eqn = diff(y,x,2) == -x*y;
y(x) = dsolve(eqn);
y = simplify(y);