Consider the following initial-value problem (IVP): dy x dx = y - x dx y(1) = 1 A.5.a. Find the implicit solution to the IVP. A.5.b. Find the explicit solution to the IVP, and verify by substitution that the solution satisfies the ODE.

Q: 1. Solve the following first-order equation: (2.ry +3y?)dr - (2ay+a)dy = 0. %3D

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Q: Q2.1 Solve the following ODE 2x²+3x sec² y dy dx Response: =

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Q: 2. (x2 + 2ху — 4у?)dx — (x? — 8ху — 4y?)dy %3D0 - - -

A: Given:                                 x2+2xy-4y2dx-x2-8xy-4y2dy=0       .........(1) First we check…

Q: Perform one iteration of Midpoint method for the following ODE. * = a e* + cy where a = 3, b = 4,…

A: Given-  A Ordinary Differential Equation: dydt=a.ebt+cy Where a=3, b=4 and c=2 Hence the ODE become:…

Q: B Solve the following D.E y(6y² – x-1)dx+ 2.xdy = 0, y(6) =1.

A: Given: y(6y2-x-1)dx+2xdy=0, y(6)=1 The given differential equation is a bernoullie differential…

Q: Compute the values of dy and Ay for the function y = e3x + 3x given x = 0 and Ax dx = 0.02. Round…

A: Please find attachment

Q: If a function y = f(x) satisfies = y, %3D then %3D dr y = e".

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Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: 3. Display an argument to show that the Gamma Function is defined for s> 0. T(s) = f e-¹4³-1 dt. 0

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Q: Among the values of x for which V(x)=0V(x)=0, which are physically possible?

A: As per previous solution The volume of box

Q: L Solve for ) for each of the following implicit functions. Simplify your answer if possible. 1 r+…

A: Given, 1 . x3+2x²y-3xy²= xy  2 .  x(x + y)²-(1-y)³ = xy

Q: III. Solve each of the following: 3. (x - y - 2)dx + (3x + y − 10) dx = 0

A: Solution is given below: