Question

Can you please explain the solution for this

Answer 1

please explain how well achieve the general solution of this equation
\[\frac{ d^2y }{ dx^2 }+y=0\]

Answer 2

@Nishant_Garg

Answer 3

\[\frac{d^2y}{dx^2}=-y\]\[\frac{d^2y}{y}=-dx^2\]
after that I've no idea, I think you would integrate both the sides 2 times, but I could be wrong @perl help :p

Answer 4

@mathmath333

Answer 5

there are some examples here
http://tutorial.math.lamar.edu/Classes/DE/HOHomogeneousDE.aspx

Answer 6

First we solve the characteristic equation associated with this diff. equation
r^2 + 1 = 0
this gives us complex solutions i, -i

Answer 7

with me so far?

Answer 8

yep

Answer 9

good luck with the problem @LilySwan

Answer 10

when you have a complex roots to the characteristic solution
r = a + bi, the solution will be the form,
y = c_1*e^(a*x) cos(bx) + c_2*e^(ax)*sin(bx)

Answer 11

\(\large \begin{align} \color{black}{\dfrac{ d^2y }{ dx^2 }+y =0\hspace{.33em}\\~\\
\dfrac{ d^2y }{ dx^2 }+y =0\hspace{.33em}\\~\\
\normalsize \text{substitue} y=e^{rx} \hspace{.33em}\\~\\
\dfrac{ d^2e^{rx} }{ dx^2 }+e^{rx} =0\hspace{.33em}\\~\\
r^2e^{rx}+e^{rx} =0\hspace{.33em}\\~\\
r^2+1 =0...........(e^{rx}\neq 0)\hspace{.33em}\\~\\
}\end{align}\)


that is prequel to perl's equation