Question

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

Answer 1

The 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\[e^{\lambda x}(\lambda^2-1)=0 \rightarrow \lambda = \pm 1\]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.

Answer 2

thank you very much...

Answer 3

You're welcome.

Answer 4

-d/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?