linear equation & linear algebra question: i need help with
2nd order differential equations

Question

linear equation & linear algebra question: i need help with 
2nd order differential equations

adunb8 · Answer

$$[d^2x/dt^2 = 2dx/dt + 2]$$

anonymous · Answer

Wave function?

lgbasallote · Answer

find x?

unklerhaukus · Answer

$$\ddot x=2\dot x+2$$$$\ddot x-2\dot x=2$$
$$m^2-2m=0$$$$m(m-2)=0$$$$m_{1,2}=0,2$$
$$x_c=c_1e^{0x}+c_2e^{2x}$$$$\qquad=c_1+c_2e^{2x}$$

anonymous · Answer

Ah yes, the characteristic equation. Good call.

adunb8 · Answer

wave function?

anonymous · Answer

Never mind, thought it looked like x'' = x for a second.

anonymous · Answer

Ugh, sorry, x''+x=0 is what I was imagining. Sorry it's been a while since I've tried these.

anonymous · Answer

But, anyway, this was billed as a linear equations/linear algebra question.
?

unklerhaukus · Answer

$$\ddot x_p-2\dot x_p=2$$
$$x_p=c_3x,\qquad \dot x_p=c_3, \qquad\ddot x_p=0,$$
$$0-2c_3=2$$$$c_3=-1$$
$$x_p=-x,$$

unklerhaukus · Answer

$$x(t)=x_c+x_p$$

unklerhaukus · Answer

could  you follow what i did @adunb8?

adunb8 · Answer

um... im lost

unklerhaukus · Answer

which bit,

adunb8 · Answer

what the teacher wants me to do is to turn into 1st order differential equation

unklerhaukus · Answer

oh, ok,

so     $\ddot x=2\dot x+2$

is independent of $t$ ,


let $$\dot x=p$$
$$\ddot x=p\frac{\text d p}{\text dx}$$

adunb8 · Answer

hm...

adunb8 · Answer

okay thanks i will try out and see if it works out