solve the following P.D.E: azu ди + u at u(0, t) = u(1, t) = 0 %3D || (1, 0< x < 1/2 0,1/2 < x < 1 u(x, o) = %3D

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Q: y" – 2y' = e*

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. S 1, 0sx s 1 x > 1…

A: Given that dydx+y=fx  , y0=1  fx=1  ,0≤x≤1-1    x&gt;1Solution:When 0≤x≤1dydx+y=1 this is the linear…

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

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Q: 2. Give the general solution of xy'dy = (x³ +y³)dx in explicit form.

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Q: Find a general solution of each reducible second-order differ- ential equation yy" + (y')² = 0

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Q: 2.Find the solution to dx using h=0.1 and h=0.05 Estimate the accuracy of second computation ²-y²,…

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A: Consider the provided question, d2ydx2=3x, 0&lt;x&lt;1and y0=0 and y1=1

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Q: 2nd Case (IBVP Summary) (Ut = 1.5uxx, 0 0 Ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) = 80°F, 0<…

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Q: 4. Verify that the solution of the DE d²x dt² + k²x = 0 is x = sin(kt).

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Q: 3- Find non-zedo solution ofs dy

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + y = f(x), y(0)…

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Q: 1. Use the Chain Rule to find 1. y = u² + 1 dy dx (show your complete solution) . u = x² - 1

A: dydx=4x3-4x

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Q: Find the Bolution to the initial value problem. | -y = 2€ %3D %3D

A: Given IVPy'''-y'=2e-t+9e2t  ; y(0)=0 ,  y'(0)=-1   , y"(0)=2 to find the the general solution use…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.