1. Use the method of variation of parameters to find the solution of 2 d²y dy dx² dx X- with What is the maximal domain of existence of the solution? २२ - 3y = 4x³, y(1) = 0 and dy dx (1) = 5.

Q: Find the general solution of the equation x(y2 + 1)dx + (1+ x²)dy = 0. A. In(x2 + 1) + 2Arctan y = c…

A: The given equation is; x(y2+1)dx + (1+x2)dy =0

Q: Find a fundamental set of solutions {y₁(x), y2(x)} of the equation y₁(x) = Y₂(x) = dx² + 13 dy d.x +…

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Q: (y + 1)dx + (4x – y)dy = 0

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Q: When I was considering what to do with my $10,000 lottery winnings, my broker suggested that I…

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Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D x² +x – 6' has a…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,∂f∂y=0,…

Q: B: Solve the following equation by Finite Differences Method, choose h = 0.25 d²y dx²-y=x+y ' y(0) =…

A: Step 1:Step 2:Step 3:Step 4: Reduced echelon form step:

Q: Show that the given function y = 5e²x + x is a solution of the IVP 2x subjected to the condition…

A: The given initial value problem dydx-2y=1-2x subject to the condition y0=5 We have to show that…

Q: The solution of (y + x + 5)dy = (y – x + 1) dx is %3D

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: a) Find a function ƒ such that f'(x) = 4x² – 2x – 1 and f (-1) = 2 %3D b) Find the function g such…

A: Given: f'x=4x2-2x-1, f-1=2 for finding functionfx, we integrate f'x so,…

Q: 3x²=ay² + (1-4x4) dy = 0 (₁ 2. 1 + x³y² +y + xy = 0

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Q: ) (2х +1) 3 —) (х+2у) — 1,. - 4x + 2у.

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Q: find general solution (x − 3y + 5)dx + (3x − 9y − 6)dy = 0

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Q: method of variation x² d²y dx² - X dy d.x of parameters - 3y = 4x³, to find the solution of with…

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Q: The solution to (2x – 4y – 3)dy = (x- 2y)dx is:

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Q: for the implicit equation zey +In(y) = x³-12? da dy 3x2 02-2 = xey + Y 3x² - ey dy da xey + What is…

A: Topic = Derivative

Q: y = V1 -— 2х

A: Our Aim is to differentiate the expression given below:-y=x41-2x

Q: (x +Jy?+1) dx x-(y- dy = 0 り*+1

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Q: 2 3. (a) Calculate dx. 1+ 4x2 8x (b) Calculate dx. + 4x² 2 — 8х dx. 1+ 4x2 (c) Use (a) and (b) to…

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Q: Q6/Use Runge-Kutta method to solve (dy/dx = x³ + y2), y(0) = land h= 0.2, find y(1)

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Q: Solve the problem by using Exact DE 3 1. (2 x³ x y² - 2y + 3) dx − (x² y + 2 x) dy = 0

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Q: a) Find a function f such that f'(x) = 4x2 – 2x – 1 and f(-1) = 2 %3D 2x b) Find the function g such…

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Q: Find the general solution of the equation: G + 6x) dx + (In x – 2) dy = 0 (x > 0) -

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Q: 2. Separation of Variables:Solve the equation (1 + y² ) dx + (1 + x² ) dy = 0 , if x = 0, y = -1

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Q: By using appropiate substitution, solve dy hpT i. x2 dx 1 = xy – y² ii. – 2. (2х + у)е2»+у | dx

A: Consider the provided question, (b) (i)

Q: Determine the general solution of y = (3y³ + x) dy/dx & give the method of solution

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Q: (14) = (x – y + 5)? dx dy %3D dy (15) (x² – y²)" – xy = 0 dx dy (16) 2xy = x² + 2y² %3D dx

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