Solve the initial value problem y(3x? – 1)dx + (x – x+ 3y)dy = 0, y(0) = 1 %3D Select one: O 2a°y – 2xy + 3y = 4 | O 2°y – 3xy + 3y = 4 %3D O 2x°y + 3xy + 3y = 4 2a°y + 2xy + 3y = 4 O none of the given answers is true

Q: 4. (x² + y2)dx + 2xydy

A: To solve the given differential equation

Q: 10. dy_x²-3y² 2xy dx

A: 10. dydx = x2 - 3y22xyit is homogeneous equation with degree 2

Q: (x + y) dx + (3x + 3y - 4) dy = 0

A: given differential equation  x+ydx+3x+3y-4dy=0 solution let y+x=u differentiate dy=du-dx…

Q: Solve the given equation.. (3x2 + y)dx + (x²y – x)dy =0 Y +3x = C a. b. x²y? + x²y+ x4 = C C. d.…

A:

Q: Solve the following DE: (1+ y² + xy²) dx + (x²y + y + 2xy) dy=0 O 2x+y²(1+x)² = C O 2y² + x²(1+x)²=c…

A:

Q: Find the particular solution of the given D.E. (y²-2xy + 6x) dx + (2xy - x²-2) dy. =0 when X=-2 and…

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Q: Solve for y. – 6y + 5( – 3y+ 8) = – 5 – 2( – 2 – y) %3D

A: - 6y + 5 (-3y + 8) = -5 - 2(-2 - y) -6y - 15y + 40 = -5 + 4 + 2y -21y + 40 = -1 +2y

Q: Solve the following equations. 1. (xy + y²)dx-x²dy = 0

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Q: x² + 4y² = C(x+y)

A:

Q: Obtain the general solution of the following equations:    2y(x2-y+x)dx-(x2-2y)dy=0

A:

Q: 3. Consider the equation (3x2 + 3y? + 6) dx + (kxy + 8y³ + 1) dy = 0. (a) Determine the value of the…

A: The solution is given as

Q: Solve the equation subject to the given condition. dy 2 dx x +y-8e", y(1)-2

A:

Q: (2y² +4x²)dx- xydy 0 y(1)= -2

A: We have to use suitable assumption.

Q: Obtain the general solution of the following equations:   (x-4y-9)dx-(4x+y-2)dy=0

A:

Q: 3s +7 Find the inverse Laplace transform of F(s) s2 + 7s + 12 f(t) =

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Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 O A. O B. O U ev O D.y O E.…

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Q: 5. dy 0sec(y/0) + y de Ө

A: 6. dydθ = θsec( yθ ) + yθ

Q: аль Ихх solve и и(o,t) =и (100,t) =o 2 и(x, 0) = 60 чо осхето so<x<100

A: The given problem is to solve the given heat equation partial differential equation with given…

Q: I Solve the fllowing FODF 2y(x+y+2) dx + (y²-x²_ 4x-1)dy = o when x=2,y= 3

A:

Q: 2. Determine C when x-y%3D0 show the solutions. (xy + x)dx = (x²y2 + x² + y2 + 1)dy

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Q: What is the degree of vertex B? Graph 2 6 10 4

A:

Q: #

A:

Q: 3X (02-60,9)y=e" (x+2) %3D

A: Given differential equation is  (D^2 - 6D + 9)y = e^3x(x+2)

Q: Obtain a family of solutions. 1. (x-y)(4x+y) dx + x(5x-y) dy =0 Ans: x(y+x)² = c(y-2x) Show complete…

A: Given: The differential equation is given as (x-y)(4x+y)dx+x(5x-y)dy=0. The aim is to find the…

Q: dy dx 2x-3y-19 3æ+12

A:

Q: (6x + y?)dx + (2xy – 3y?)dy = 0

A: Image is attached with detailed solution.

Q: Question 12 Find the solution. dy 2y -2xy dx Ay = x2(x+c)2 By = x(x+c) ©y = x?(x-c)-2 Dy = x (x+c) 3

A: Given Differential equation is dy/dx - 2y/x = 2xy1/2

Q: 7. The particular solution of (D³ + 2 D²-5D-6)y = 0, when x = 0, y = 0, y = 0, y" = 1

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Q: 7. dx dy 4y - 3x 2x-y

A:

Q: 3. (y² - xy)dx + x²dy = 0

A:

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.