The function def ined by y=Acos(In(x)) +Bsin(In(x)) d²y dy is the solution of the following DE: x²- dx2 +x - +y=0 dx صواب İhi

Q: Solve the following differantial equation using finite difference method. d²x(1) + x(t) = 0 dt? dx…

A: Consider the given DE and finite difference formula for the function x(t).

Q: Find the solution. Zy dx = (-1dx - dy) A (x-1)x = (y+1Xc - 2x - In|y-1|) B (x-1)y = (x+1Xc +x -…

A: First re-arrange the given differential equation. 2y dx=x2-1dx-dy2yx2-1=dx-dydxdydx+2yx2-1=1

Q: Find the solution of y- dy --x = 0 using separable variable method. dx +C 2 3 Ob. None of these y +C…

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Q: Find the antiderivative F(x) that satisfies the given condition. dF dx = 4e* + 4x²; F(0) = -5

A: Given query is to solve the differential equation.

Q: Find the solution using Variation of parameter. (D²1)y=e* + 1 1 y=C₁e* + C₂e-x+ 를xex ex-1 2 4 1 1 -X…

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Q: Which of the following is the particular solution to the DE y(9x-2y)dx- x(6x-y)dy 0; y(1) 1? A.…

A: Given equation is --(1) We are to need to find the particular solution indicated. The function…

Q: dy Find the particular solution: 2xy + (1+x2) ) = 0, y(0) = 1 . %3D dx O A. y = In(1+ x²) O B. None…

A: We have to find the particular solution

Q: Test for the exactness and find the implicit solution to [2x+ycos(xy)]dx+ xcos(xy)dy=0when -플.y=1. X…

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Q: In each exercise, obtain the particular of solution. a. (y + Vx2 + y²) dx – x dy = 0; when x = V3, y…

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Q: Find fæxyzz for f(x, y, z) = z³y² ln(x). [Show your solution.] Select one: O O O x² 6z²y x² 2z³y x²…

A: See this solution in below.

Q: A: Compute dy at (2, 1) where y = xcos2x dx B: Solve for x: a2 (y³ + vx-4 +y sin2x) < 4cos2r Тдхду…

A: Please see the answer below.

Q: Find the general solution of (1+ cosy)dx - xsin ydy = 0. a. X - sin y - x cos y = C b. x + sin y +…

A: The solution is given as

Q: 2. y(x4-y²)dx + x(x++y²)dy = 0

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Q: 3. Is y(x) = C,sin2x + C2cos2x, where C1 and C2are arbitrary constants, a solution of y" + 4y = 0?

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Q: 2 show that V(x, y) = x 'f (2x+y) is the general Solution of : Xav dx 2x du ду = V

A: We can show given function is a solution of the given equation .

Q: Þ(x) = x² is an explicit solution to dy 2y dx ylgn ihi

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Q: The given DE is homogenous t(s² + t²)ds = s(s² – t²)dt obtain its solution by substituting t=sv.

A: Please see the answer below

Q: In each exercise, obtain the particular of solution. a. xy dx + 2(r? + 2y?) dy = 0; when x 0, y = 1

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Q: Let y(x) be the solution for the DE : У 3 (х +у-1)2 If y(0) = 1, then find y() 8 - JT JT Зл 4 Зл -…

A: Here to solve the given differential equation first we change the variable y by a  transformation .…

Q: 1 du k at dx² d'u where his positive constant. : 00 Find the solution of IBVP: u(0,1)=0;…

A: As per the question we are given an IBVP in the form of a heat equation, and we have to solve it to…

Q: dy +2(x+1)y² = 0 y(0) =-% Give the largest interval I on which the solution is defined. dx (6) 4. 8,

A: Given equation is: y'+2x+1y2=0, y0=-18

Q: Find the Particular solution of the ODE d?y dy -6--7y = -9e-2x, dx2 at y(0) = -2 and y(0) = -13 %3D…

A: We have to find the particular solution of the ODE                       d2ydx2-6dydx-7y=-9e-2x at…

Q: Determine whether the DE is exact then find the implicit solution. 3y(x²-1)dx + (x3 +8y-3x) dy=0; x…

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Q: Which of the following is a Bernoulli's Equation? y^2 dx + (3xy + y^2 - 1) dy = 0 y (x^3 x^xy) dx…

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Q: i) ais f(x,y) = x2 + 3xy + y -1 Laalic * Te Te

A: Given that  Af(x,y)=x^2+3xy+y-1  To find the partial differentiation of f(x,y)

Q: Let f(x,y) = C be the solution of the DE 2e3cos(vin(x)dx-3xsin(y)e3cos(in(x))-dy%3D0, where (x,y)…

A: We need to find value of C.

Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

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Q: Test for exactness and determine the particular solution of: (yexy – 2y³)dx+ (xexy – 6xy2 – 2y)dy =…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the particular solution of the DE x?dx +ydy =0, when x = 2, y 1. O 2x3 + 3y2 = 19 O 2y + 3x2 =…

A: Given, differential equation,x2dx + ydy = 0Integrating on both sides, we get∫x2dx + ∫ydy = Cx33 +…

Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx - (3x- y – 4)dy = 0 %3D

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Q: solution of the di dy x + 4y = * x2

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Q: Find the general solution of the DE x(y? + x)dy - y(y?- x²)dx% = 0. %3D (x-y) In x +y In y =cx + y O…

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Q: Solve the following using Integrating Factor by Formulas. a.) 2y(x2 - y + x)dx + (x2 - 2y)dy…

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Q: What is the solution of (xy? – x) dx + (a²y + y) dy = 0 when x = 0 and y = 3 %3D O (22 - 1) (y² – 1)…

A: Exact differential equations.

Q: The particular solution of x dy - y dx when x = 1, y = 3 is a. y + x2 – 1 = 3x b. y + 2x2 + 1 = 6x –…

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Q: Find the general solution: k^2 dx+(x-y+k)^2 dy=0 O A. y+k arctan [(x-y+k)/k)=c] O B. tan…

A: Given differential equation  k2 dx+x-y+k^2 dy=0

Q: B. In each exercise, obtain the particular of solution. (y+ Vx² + y²) dx – x dy = 0; when x = /3, y…

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Q: 2. Given the DE as (x² + y² – 3)dx – 2xydy = 0 a) Prove if the given DE is exact or non-exact b)…

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Q: 2) Obtain a particular solution for d*y d?y dy + +y = x³ + 2x +1 dx4

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Q: - Find the solution of the separable DE 2ydy = (x + 1)dx. a. y- +x x+c c y=x'+x+C d. y=x + 3x + C b.…

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Q: If y = f(x) is the solution of (-12ay+ 2x)dx + (-4x³ – 48y?)dy = 0, f(0) = -1, then %3D Lütfen…

A: The equation is exact so we can solve directly

Q: 3. Find the complete solution of (x²y+y³ – y)dx + (x³ + xy? + x)dy = 0 Hint: Expand and Simplify

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Q: find 04 O B O 7 O -12 af ду dy' given f (x, y) = e + 2xy² – 4y at (0, 3) -

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Q: dx - is 2/x - Sin| x +s|+c. Vx +5 The antiderivativeof - A) True B False

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Q: The antiderivative of [Vx-25 dx is V x2 - 25 - sec-x+ C. A True B False

A: Given: I=∫x2-25xdx     As we know from the trigonometric identities; 1). sec2x=tan2x+1 2).…

Q: ydx + x(Inx - lIny - 1) dy = 0, when x = 1, y = e %3D

A: Given :     ydx+xlnx-lny-1dy=0,        when x = 1 , y = e that means y1=e

Q: 3y(x2 - 1)dx+(x +8y–3x)dy= 0 when x= 0, y=1 |

A: Given: 3y(x2 −1)dx+(x3 +8y−3x)dy= 0 when x= 0, y=1

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.