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anonymous
 5 years ago
Can anyone help me to solve this differential equation: (d/dx)(15*dT(X)/dX)+15*T(x)=528.75
anonymous
 5 years ago
Can anyone help me to solve this differential equation: (d/dx)(15*dT(X)/dX)+15*T(x)=528.75

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The LHS is:\[\frac{d}{dx}\left( 15\frac{dT}{dx} \right)+15T=15\frac{d^2T}{dx^2}+15T\]so, letting 528.75=c, and dividing both sides by 15, you have,\[T''T=\frac{c}{15} \rightarrow T''\left( T\frac{c}{15} \right)=0\]Let\[v=T\frac{c}{15} \]then\[v''=T''\]and you have\[v''v=0\]which is first order, homogeneous, with constant coefficients, so you can assume a solution of the form\[v=e^{\lambda x}\]Hence\[v''=\lambda^2 e^{\lambda x}\]and substituting into the d.e., we have\[e^{\lambda x}(\lambda^21)=0 \rightarrow \lambda = \pm 1\]So the solution is\[v=c_1e^x+c_2e^{x}\]But \[v=T\frac{c}{15}\]so\[T=c_1e^x+c_2e^{x}+\frac{c}{15}\]where c=528.75.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you very much...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0d/dx(15*(dT/dx))d/dy(15*(dt/dy))=30 about this D.E. i can do the same steps like for the previews one?
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