3. Which of the following equations is a variable separable differential equation? а. (х +x?у)dy %3D (2х + ху?)dx b. (x + y)dx – 2ydy = 0 c. 2ydx = (x² + 1)dy d. y?dx + (2x — Зу)dy %3D 0

Q: Find the solution. y'+=V5.y(1) = 0

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Q: dy 4. x - y = x² sin x dx

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Q: 2хy -y' y2-x2 a. 3yx? + y3 = k Зух? — Зу3 c. 3yx? - y3 =k d. yx? – y = k e. Not in the list. b. %3D…

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Q: * jax vnen 8. xy dx + 2(x² + 2y²)dy = 0 ; when x = 0, y = 1

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Q: What is the particular solution to the differential equation (1-xy)? + (y² + (1-xy)- )dy = 0 and y =…

A: Givendx1-xy2 + y2 + x21-xy2dy = 0withy(4) = 1

Q: 18. (Зx?у — Зу)dx + (х3 + 8у — 3х)dy 3 0 19. (х — у)dx + (3х + у)dy 3D 0 %3D

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Q: If y' = х-у then its solution is x+y'

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Q: (y + Jx² + y² )dx – x dy = 0 ; when x = v3,y = 1 7.

A: The given problem is to solve the linear differential equation with given initial conditions. We…

Q: c. Determine the truth value of each of these statements if the universe of discourse of each…

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Q: 2. (3ху + Зу — 4) dx + (х + 1)? dy %3D 0. ANS. у 3D 2(х + 1)-1 + c(x + 1)-3.

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Q: Choose the correct answer If x2 + y2 = 9, then y'=...  -y/x  y/x  -x/y  x/y

A: We have to find y'

Q: (3x² – 2xy + 3y²)dx = 4xy dy

A: 6. The given is  3x2-2xy+3y2dx=4xydy Thus, dydx=3x2-2xy+3y24xy.....(1) which is a homogeneous…

Q: If y = v3x , then y' is A. -1/2 B. V3 x -1/2 С. /3x V3 D. 2 V3 -1/2

A: Given y=3x

Q: y = 3xp +p 0 what is the general solution of the differential equation? dx

A: Given that y=3xp+p,  p=dydx To find the general solution: y=3xp+py=3x+1p Differentiate both sides…

Q: (4xy+5y)dx+(4x² +15xy-12y)dy=0. Use two methods.

A: Note: according to our guidelines we can answer only first question because there are multiple…

Q: b) By using the laws of set theory, show that [(A U B) n (An C)] u (B n C) = A U B.

A: Here we have to prove left hand side is equivalent to right hand side using laws of set theory

Q: x² + y² Solve y'= 2. xy 3. Solve (x+y-1)dy = (x-y-3)dx

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 7. Find the general solution: y(x? + y²)dx + x(3x² – 5y²)dy = 0 a. y³(y² – x²) = cx b. 2y3(у2 — х?)…

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Q: 8. (Зх — у — 1) dx + (9х — Зу + 4) dy %3D0

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Q: For x(t) shown below , the Laplace transform is

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Q: (ху + 1) dx + (ху — 1) dy %3D 0

A: As per the instruction, we will be answering only the first one. Here, M=xy+1 and N=xy-1. Now,…

Q: Which is the differential equation of the family of parabolas with axis along the y-axis and with a…

A: To find out the differential equation for the given statement.

Q: 5. хуdx — (x? + 3у?) dy %3D 0.

A: We know that the differential equation Mdx+Ndy=0 is exact,  if ∂M∂y=∂N∂x. The solution of the…

Q: . (D² + *. + D)y = 6 + 3 e²

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Q: Find the general solution or particular solution. 1. dy = (x-3y)dx 2. y'%3х- 2усоot 2x 3. (Зх- 1)…

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Q: From the differential equation dy = x2 dx, what is the equation of y in terms of x as the curve…

A: Given: dy=x2dx

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.