a) Find the general solution for UTM dy TM dy +2- dr? dr (1+f) UTM (77 +1)xz² = fip +

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A:

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A:

Q: dt 34. tan t/4 – sin² t dy - Vy dy 35. 36. yV3 + (In y)? x² 1 38. dx 4х + 5 37. :dx /x² + 2x + 5…

A: 34) Solve the integration:

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A: d2udx2=-x2⇒dudx=-x33+c⇒u=-x412+cx+du(0)=00=du(1)=00=-112+cc=112u(x)=112(-x4+x)

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A: Given, y'=ty+sint, y1=0, 1≤t≤2

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A: Given y'=y+xe2xand y0=1

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Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

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A:

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Q: 5 By separation of variables, Solve the followin PDES :- du dt d2u dx2 @ o U (0₂t) =(4,t) = G u(x,0)…

A: Given is the Partial Differential equation ∂u∂t=2∂2u∂x2…

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Q: find the suprimum, in! infimum maximum and minimum of { c,1": (1+):ne w}, if t)ine w}

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Q: 1.2 Exercises a. Show that ¢ (x) = x2 is an explicit solution to 1. dy = 2y dx

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Q: Using the approximation dy dy * Yn+1 - Y, and that dr 1, y = 2 dr h when r= 0. Then, y, = A h-2 h+2…

A: Use the approximation hdydxn≈yn+1-yn and that dydx=1, y=2 when x=0. Then y1=?

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Q: #3. Solve the fallowing Caucly problem in R" x(0,0) U4-Ou t cu = 0 u =9 On IR"x{t =0}. where c is a…

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A: Using differentiation

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Q: Q1. Solve the follounig ordinary diflerential agethins, 2 ci) dy ;If yoo when x=0 = xe dx dy + Cot y…

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Q: Determine the solution of y dt + (2yt + I) dy -Ogiven that given that y (-1) = Q

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A: