[pswpswpsw]

wave equation:

d2u/dt2=a^2*d2u/dx2 eq(1)

singe wave equation

du/dt+c*du/dx=0 eq(2)

eq(1) can be derived to eq(2).

But I don't know if eq(2) can be derived to eq(1)

Thanks for reading.

Shaowu

[FMDenaro]

Originally Posted by pswpswpsw

wave equation:

d2u/dt2=a^2*d2u/dx2 eq(1)

singe wave equation

du/dt+c*du/dx=0 eq(2)

eq(1) can be derived to eq(2).

But I don't know if eq(2) can be derived to eq(1)

Thanks for reading.

Shaowu

if you further derive the (2)

d2u/dt2 + c d/dt du/dx = 0 -> d2u/dt2 + c d/dx du/dt =0

hence

d2u/dt2 + c d/dx (-c du/dx) =0

In general a second order equation can be written as a system of two first order equation