Solve the following PDES by separation of variable metho (i): u +U, = 0 (ii): y'u, –x’u, = ди (iil) : хи, +2уи %3D0 (iv): =c² ốt ôx? (v):и, — 2и, —и

Q: 7. y - y = 16

A: The objective is to find the general solution .

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

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Q: (2xy² + 2y) + (2x²y + 2x)y' = 0

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Q: 8. y" – y = 5sin²(x); when y(0) = 2, y'(0) = -4 %D

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Q: 3 23x-1 rewrite y=

A: Given: y=3x-13. To find: y' Solution: We know that, xn=x1n Therefore, given equation can be…

Q: 3x гу у II 2 ху

A: 3x2-2y2y'=2xy We can write as y'=2xy3x2-2y2=2yx3-2yx2 Clearly its homogeneous differential equation…

Q: Let y = Arcsec (cos² 3x). If y '= == A (B C) D) - 6 tan3x - 3 sin3x - 6 sin3x cos3x N 2 cos3x D and…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: y = x"^, x > 0 Inx-1 Inx Inx C. y'= 2lnx x' „Inx-1 D. y'= 2lnx x" „Inx-1 A. y'= x B. y'= 2 x'

A: SOLUTION-

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: X = y + % y = 0.000396707 – 0.24576 x2 22 = 0.00029753 - 0.12288 x²

A:

Q: y"" + 3y'' − 4y = 0. Find y . Please check the equation carefully and then start

A: We have given equation y''''+3y''-4y=0   Auxiliary equation of differential equation is  m4+3m2-4=0…

Q: find sol. y'- y =y2e-x

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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: If xy? - y3 = 5, find y'. y' =

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Q: The general solution of y' = X У can be written in the form = C

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Q: Differentiate: y = (3x 교-5z) (4n3 +2) O y' = 60a + 80a- 12a 10 - O y' = 60x + 80a + 12x O y' = 60x4…

A: Let's find.

Q: In Calculus you will see the symbol y'. Treat y' as a variable and solve the equation for y. 6y²y +…

A: To solve the following equation for y'. 6y2y'+30xy+6x2y'=5y2+25xyy'

Q: Differentiate y = (2х + 1) а. 2 y = (2х + 1) b. 1 y = 2/(2х + 1) 1 y = (2х + 1) d. y = (2х + 1) е.…

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

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Q: 9. y(x² + y²) dx + x(3x² – 5y²)dy = 0 ; when x = 2, y = 1

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Q: y = Vx – 1 А. Domain: х —1 Range : y 20 С. Domain: х >0 Range : y > -1 D. Domain: х >1 Range : y >…

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Q: Determine the equation whose y'= Y/3x. 3x2 = y3 A 1 у? y= 3 x2 © x² = y3 1

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Q: 1.² T 20 40x-x² 9√x²+y2 dydx=

A: We have to solve ∫020∫x40-x29x2+y2dydxThe region bounded by0≤x≤20x≤y≤40x-x2⇒x=y and y=40x-x2squaring…

Q: j'+7y'+12y=2le", y(0); (0)=,"'(0)= -10. 10)=-10 .

A:

Q: 2. у' %3D х3 — 2ху when x = 1 & y = 2

A: This is a problem of differential equation.  Here we will substitute the some of variable and then…

Q: 4. (3x – y)2 = 6x + 2y + 23 @ (1,-2) 5. x(x² – y²) = 3 @ (-1,2)

A: 4) (3x-y)2=6x+2y+23, @(1,-2) 5)x(x2-y2)=3, @(-1,2).

Q: If y= (x³ + 1)* , then y' = ? A) None of the given choices В 6x²(x³ + 1) O (3x2)2 D D 2(3x²+1) E…

A: Given:- y = (x3+1)2 To find:- y'

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.