The differential operator (D – 8)(D+2)y= O (D² – 6D + 16) y O d'y 16y | dæ² dx O (D² + 6D – 16) y (Dy – 8y)(Dy+ 2y) =

Q: dy will be dx In x+1 If y = then 2x3 - 3x' (2x- 3x) +1)- (In x+ 1)(6x? – 3) (2x – 3x)? A. (2x - 3x)…

A: To find the dy/dx of the given function

Q: dy xy+3x-y-3 dx xy-2x+4y-8 - 5 Ans: yx + In n (x+4) ³ =

A: Given that the differential equation dydx=xy+3x-y-3xy-2x+4y-8

Q: x²V4x +1 dy then dx If y = In (x³ + 5)3

A:

Q: dy xy+3x-y-3 dx xy-2x+4y-8 - - In (²+4) ³ = Ans: y-x + In y+3, = C

A: The given differential equation is dydx=xy+3x-y-3xy-2x+4y-8 We have to find the general solution of…

Q: ( 3u + 3uv – 4)dv + (v+1)*du =0

A: Given that: (3u+3uv-4)dv+(v+1)2du=0

Q: y² (y + 2)ï dy

A:

Q: Reduce the linear DE (2xy + x²+x¹) dx − (1+x²)dy=0 to standard form (A) +y−2x)=x?(1+x2 dx dy B…

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Q: Integrate/Evaluate the following: (a) (b) √₁44+5y2 dy y³+4y ƒ (y+1)dy y³-1

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Q: 3. Use Green's Theorem to evaluate J(* -6y)dx+(y +10y)dy where C is shown below.

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Q: 1-y2 Q2: Evaluate i y² (x? + y²)dx dy

A:

Q: Find Cyy(x.y) if C(x.y) = 9x² + 5xy – 2y²+4x-4y-8. Cy (x.y) =D

A:

Q: 1 (D² – 3D + 2)y 1+e¬x

A:

Q: ( 2x + 3y)dx + (3x – 2y)dy = 0 O x² – 3xy – y² = C 2. h O x² + 3xy – y² = C 2. x²- 3xy + y =C x² +…

A: Exact differential equation

Q: 2. Evaluate a 2а-х У — х dx 4a² + (x + y)² ° using the transformation of coordinates u = x + y, v =…

A: Consider the given information:

Q: (x– 3)dx J (x² + 2x+ 4)²

A:

Q: y = V1 -— 2х

A: Our Aim is to differentiate the expression given below:-y=x41-2x

Q: se Green's Theorem to evaluate SC (5y-9x)dy-(yx-x³)dx where C is shown below

A: Follow the procedure given below.

Q: Write the linear DE of order one x²dy + (2xy-x+1) dx=0 in standard form A B D dy dx dy dx 1 2 +y(-)…

A:

Q: Find the total differential. 8x + y 3z - 2y dw = W = 8 3z-2y dx + 3z- - 4y - 16x (3z-2y)² Jdy + (7…

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Q: Solve for the higher order DE number 2

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Q: 2. (x² + y² + 1)dx + x(x − 2y)dy = 0

A:

Q: (4+y- sy³)ldy Vỹ 3

A: To evaluate the given integral.

Q: dy xy+3x-y-3 dx xy-2x+4y-8 = Ans: y - x + In (²+1) ³ =C

A: We want solve the following differential equation.

Q: Find (y - 1)(3y² - 2y + 1) [(y - 1) (34² dy. +1

A: We are required to find: ∫(y-1)(3y2-2y+1)y2+1dy

Q: y²dx+x(x+y) dy=0 A xy²=c(x+2y) B x²y=c(x+2y) © xy²=c(2xy) x+y²=c(2xy)

A:

Q: 3 Evaluate: ³₂²₁²[z³(x + y)³] dz dy dx

A: When a triple integral is performed, then the innermost variable is integrated first, then the…

Q: If x = t+1 and y = t2 - 2t +3, then find t - 1 dx

A: We can find the answer using required rules as below.

Q: (1 – xy)-²dx + [y² + x²(1 – xy)¯²]dy = 0; when x = 2, y = 1

A:

Q: y′ = t2 + y2

A: