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Find the temperature function $T(x, y)$ in the infinite strip $0<y<pi$ that satisfies the boundary conditions in Figure $10.30 .$ Hint: Use $w=e^{z}$. $$ egi...

Question

Find the temperature function $T(x, y)$ in the infinite strip $0<y<pi$ that satisfies the boundary conditions in Figure $10.30 .$ Hint: Use $w=e^{z}$. $$ egin{array}{ll} T(x, 0)=50 & ext { for } x>0 \ T(x, pi)=-50 & ext { for } x>0 \ frac{partial T}{partial n}=T_{3}(x, 0)=0 & ext { for } x<0 \ frac{partial T}{partial n}=T_{y}(x, pi)=0 & ext { for } x<0 end{array} $$

Find the temperature function $T(x, y)$ in the infinite strip $0<y<pi$ that satisfies the boundary conditions in Figure $10.30 .$ Hint: Use $w=e^{z}$. $$ egin{array}{ll} T(x, 0)=50 & ext { for } x>0 \ T(x, pi)=-50 & ext { for } x>0 \ frac{partial T}{partial n}=T_{3}(x, 0)=0 & ext { for } x<0 \ frac{partial T}{partial n}=T_{y}(x, pi)=0 & ext { for } x<0 end{array} $$



Answers

Find the solution of the differential equation that satisfies the given initial condition.
$ y' \tan x = a + y, y(\pi/3) = a, 0 < x < \pi/2 $


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