1. The function u(x, y) = e cos y is a solution of: %3D a) dx² dy? b) = 0 dy? Pu c) + 4- d) None of the above.

Q: x d²y dx² + 2 dy dx Sinx + xy = 0, gıe six → ygo? = X

A: First let us find the second solution of given differential equations.

Q: Determine the particular solution. (2xy)dx = (y² – x²)dy × = 1, y = -2 2 = 3x3y + y3 O 3 = 3x?y + y3…

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Q: dy 2. (a) Determine in terms of x and y given that dx i. x²y + 3xy3 – x = 3 ii. sin(x? y?) = x (b)…

A: Let's find.

Q: w = x Tan (yz), x = u2, y = e2v , z = v cos u. Find wu and wv 10.

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Q: SHOW THE SOLUTION OF: 25 - 2xy dy CHOICES: A.) y = x'(x+c) B.) y = x(x+c)? C.) y = x(x+c) D.) y =…

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Q: 1J, (x) dx I= -J, + J, dx a O dx b O I=J, -2 I=J,+2 dx.c O I= -J, + J dx d O

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Q: 5) Solve the Non-linear second ODE: d²y + 3 x² y dx? y? = x² ) (dy %3D

A: Given: Non-linear second order differential equation is 3 x2 y d2ydx2+y2=x2(dydx)2

Q: The function f (x,y) = e* +3 tan – is a homogeneous function of degree_

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Q: 3) Show all work for the following problems. i) What is the integrating factor to the following…

A: As the given equation is first order differential equations .

Q: 2. Solve for y in terms of X for the following equations: a) In(1- 2y) = x b) In(y- 1)- In 2 = x +…

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Q: 8) Using the method of separation of variables, fine the solution of the following equation. du dx…

A: Partial differentiation is defined as the dependent variable with more than one independent…

Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

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Q: x² x dy +y=- 3 dx 3.

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Q: Evaluate the value of I = (4,0). I = Sleby. r 3x) dx + (6xe6y + y)dy, where I is the straight line…

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Q: d . Suppose r and y are variables that satisfy the equation r? – y3 = 12. What is dx dy 4x3 dx¯3y…

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Q: 2. Solve the following equations: dzy 3 dx = 9, when x 0, y = 0, = 0 a) %3D %3D dx? %3D dy b) 24y 3y…

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Q: Evaluate: IIncx + y) – dy dx 3 a² \In(2a) – –In(a) – + Ei(-a) – In(a) – In 2 +- Ei(-1) А. B. a*…

A: We are asked to evaluate the double integral:…

Q: Please solve. Thank you

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Q: 5. ( + v?Va? +y?) dx – xy /a? + y? dy = 0

A: I am attaching image so that you understand each and every step.

Q: Find the solution of dy r(1+ y?) dr 4+22

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Q: If Sf(x)dx = 5, i f(x)dx = 2, and Sif(x) dx = -1, find f(x)dx. %3D %3D А.) -2 В.) 2 С.) -3 D.) 3

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Q: In Exercises I and 2, find dy/dx. 1. y = sin (x + 1) x+ cos x x + 1 2. y =

A: As per the company guidelines, I can solve only one question.

Q: Prove that v5 is irrational.

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Q: Cl + x )y' = x"y"

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Q: (B) Solve the following simultaneous equations: dx 2-3x ++4y = e?t dt dy dy dx + 2x+2-y 0 dt dt dt

A: Given, the simultaneous equations:       2dydt-3x+dxdt+4y=e2t        dydt+2x+2dxdt-y=0

Q: d²x = y² + 1 а. y dy2 y (* + - ** + 1 dx, 2 d²x x² + 1 dy² d's d²s С. dy3 dx? () = x² + 1 dp. d. y…

A: An ordinary differential equation is an equation involving only one independent variable

Q: 3 4 t | Q2. a) Suppose A =| 2 1 -4 |and b(t) = | 0 |, then find the sol 1 2 -t² dX = AX and (ii) dt…

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