Simple partial differential equation

[dexter90]

Hello.

I have equation:

\frac{\partial T}{\partial t}-\frac{1}{2}\cdot \frac{(\partial)^2 T}{\partial x^2}=0

I calculated determinant:

\Delta=(-\frac{1}{2})^2)-4\cdot 1 \cdot 0 \Rightarrow \sqrt{\Delta}=\frac{1}{2} \\ (\frac{dT}{dt})_{1}=-\frac{1}{4} \\ (\frac{dT}{dt})_{2}=\frac{1}{4}

next

T=-\frac{1}{4}t+C_{1} \Rightarrow T+\frac{1}{4}t=C_{1} \\ T=\frac{1}{4}t+C_{2} \Rightarrow T-\frac{1}{4}t=C_{2}

I am add a new coefficients \eta and \xi, then

\xi=\frac{1}{4}t+T\\ \eta=-\frac{1}{4}t+T

Then I calculated matrix jacobian's =\frac{1}{2}

Good?

I greet

Post edited

 

[HallsofIvy]

Hello.

I have equation:

\frac{\partial T}{\partial t}-\frac{1}{2}\cdot \frac{(\partial)^2 T}{\partial x^2}=0

I calculated determinant:

\Delta=(-\frac{1}{2})^2)-4\cdot 1 \cdot 0 \Rightarrow \sqrt{\Delta}=\sqrt{2} \\ (\frac{dT}{dt})_{1}=-\sqrt{2} \\ (\frac{dT}{dt})_{2}=\sqrt{2}

I'm not all that clear on what you are doing but that first statement is obviously untrue.
\Delta= (-\frac{1}{2})^2- 4\cdot 1 \cdot 0= \frac{1}{4}
so
\sqrt{\Delta}= \frac{1}{2}
not \sqrt{2}<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> next<br /> <br /> T=-\sqrt{2}t+C_{1} \Rightarrow T+\sqrt{2}t=C_{1} \\ T=\sqrt{2}t+C_{2} \Rightarrow T-\sqrt{2}t=C_{2}<br /> <br /> I am add a new coefficients \eta and \xi, then<br /> <br /> \xi=\sqrt{2}t+T\\ \eta=-\sqrt{2}t+T<br /> <br /> Then I calculated matrix jacobian's =2\sqrt{2}<br /> <br /> Good?<br /> <br /> I greet </div> </div> </blockquote>

 

[dexter90]

Thanks,

Of course, I made mistake in write. I would like solve partial differential equation but I don't have experience. I edited my post.