dy The solution of homogeneous differential equation dz + 8xe z -y -e x 8x +c %3D -e r 8x +c 8x +c -y - 8x +c %3D

Q: I) Consider the function: y = + C,e2x + C,e-5x + Czxe-5x

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Q: (xe* + 4e* + 4e' + 4 In y) dx + ( xe + dy = 0; y (0) = 0 y 6.

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Q: 2. :. (xy²+x-2y+3) dx + (x²y-2x-2y) dy = 0

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Q: Find the solution. (D² - 20 - 3)y = 0; when x = 0, y = 0, y'= 4 A y = e-e B y =e+e y = e y = -e

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Q: Find the general Solution of the Partial differential equation (xz + yz)p+ (xz- yz)q = x' + y?

A: This is Lagrang's linear equation so solve using auxiliary equation.

Q: Solve the given differential equation: (4x + y - 1)dx + (x - y - 4)dy = 0

A: given differential equation: (4x + y - 1)dx + (x - y - 4)dy = 0

Q: The integrating factor of non-exact differential equation (æ³y³ – x®)dx – (y6 – x³y)dy= 0 1 xty3 +…

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Q: (a) (x* +y*)dx + 2x³ydy = 0

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Q: Solve the homogeneous equation (3x-y) dx + (x-3y-3) dy = 0

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Q: The differential equation x*y + 3xy = 2y? + 2x? has a solution of the form f(x, y) = 2 g(x) + C.…

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Q: To reduce the differential equation with linear coefficients (x+2y-4) dx- (2x+y-5) dy=0 to a DE with…

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Q: du Solve the equation "u(0, y) = 8e» = 4. by the method of separation of variables.

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Q: Find the solution to the linear system of differential -8x - 30y equations [x¹ ly' satisfying the…

A: Solve by matrix method.

Q: Q) Determine the complete solution of the simultaneous differential equations: (D+5)x+(D+3)y=e…

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Q: The solution of the exact differential equation (2xy2-3) dx + (2x²y + 4)dy = 0 is: O None of them…

A: Ans- To solve the given differential equation, we need to check if it is exact. For that, we check…

Q: d³y d?y dx3 dx2 =0 is given by %3D The solution of the differential equation

A: Given : d3ydx3 + d2ydx2 = 0

Q: The solution of the differential equation V y +2y +y=2e* using the method of reduction of order is

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Q: sinr where 0sI<R 3. a) Evaluate LF())where F()-o where t2 dy de 3x-3y+4 and dt = 2x-2y-1 dt b) Solve…

A: see below the calculation and explanation

Q: Using the substitution y = vx and dy = v dx+ x dv, the differential equation with homogeneous…

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Q: (8x² y² -2x + 4xy² - x) dx + (2xy + x + 2y + 1) dy = 0

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Q: Determine the general solution of (x-2y)dx + (2x+y)dy = 0

A: See the details solution in below

Q: (9) Solve the following diserental equation dy dx 2 3+y 3.x 3-y = (9x - y²x), y(0) = 0 Answer: = e

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Q: Determine the solution of 2x (y+1)dx−ydy=0

A: Determine the solution of 2x (y+1)dx−ydy=0

Q: The integral given below is calculated for n = 6 by simpson 3/8 method 140000 2000ln 140000-2100t

A: Consider the provided question,

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.