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Simple partial differential equation 
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#1
May112, 02:52 PM

P: 15

Hello.
I have equation: [tex]\frac{\partial T}{\partial t}\frac{1}{2}\cdot \frac{(\partial)^2 T}{\partial x^2}=0[/tex] I calculated determinant: [tex]\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}[/tex] next [tex]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}[/tex] I am add a new coefficients [tex]\eta[/tex] and [tex]\xi[/tex], then [tex]\xi=\frac{1}{4}t+T\\ \eta=\frac{1}{4}t+T[/tex] Then I calculated matrix jacobian's =[tex]\frac{1}{2}[/tex] Good? I greet Post edited 


#2
May112, 04:11 PM

Math
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Thanks
PF Gold
P: 39,683

[tex]\Delta= (\frac{1}{2})^2 4\cdot 1 \cdot 0= \frac{1}{4}[/tex] so [tex]\sqrt{\Delta}= \frac{1}{2}[/tex] not [itex]\sqrt{2}[itex] 


#3
May212, 02:02 AM

P: 15

Thanks,
Of course, I made mistake in write. I would like solve partial differential equation but I dont have experience. I edited my post. 


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