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: Let y = (): Identify the value of d'y from the following: dx? x+1 2(1+2x) (x+1)* 2(1–2æ) (x+1)*…

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Q: Find a fundamental set of solutions {y₁(x), y2(x)} of the equation y₁(x) = Y₂(x) = dx² + 13 dy d.x +…

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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: 1-y² L In (r* + y? +

A: Introduction: The process of determining the area of the region under the curve is known as…

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: 6. x(x² - y²-x)dx + y(x² - y²)dy = 0 x=2 y= 0

A: It should be -y instead of +y.

Q: y² (y + 2)ï dy

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Q: Coefficients Linear in Two Variables (x +2y - 4)dx + (2x + y-5)dy = 0 when y(1) = 0

A: We have to find solution of given differential equation.

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: The solution to (2x – 4y – 3)dy = (x- 2y)dx is:

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Q: x²j + 3xỹ + 5y = 2 In (x)

A: Please see the attachment

Q: 7. (D5 – 2D³ – 2D² – 3D – 2)y = 0 8. (2D3 – D² + 36D – 18)y = 0; when x = 0, y = 0, y' = 2, y" = 4

A: Note:- this is multiple questions and you have not mentioned is here which question you want to…

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: Show that 2²) 2 (¡ f(x) dx + ½ (b² − a²) [[y yf(x) + xg(y)dy dx = ½¼½ (d² − c²) <²) (1 g(y)dy

A: We have to show that the given expression, ∫ab∫cdyfx+xgydydy dx=12d2-c2∫abfxdx+12b2-a2∫cdgydy.

Q: (2t – 3)·e -t²+3t dt 3 2/Inx dx . X (2у-3)12

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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: v*exp(uv)du + u*exp(uv)dv = 0

A: The given equation is, v×exp(uv)du+u×exp(uv)dv=0

Q: (x – 2) dx +4(x+y- 1) d

A: Given       (x-2)dx+4(x+y-1)dy=0

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: (4x² + y²) dx + x(x-2) dy =6 Verify that M(x,y) = 4x² + y² and N(x, y) x (x-2) are homogenous 1-

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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: (x + 2y - 1)? dx = dy A. x + Arctan { [V(2)] [(x + 2y -1)] } = c B. x = Arctan { [V(2)] [(x+2y-1)]}…

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Q: Solve the equation (2xy+ y) dæ + (x² – x) dy = 0. - O y = cx(x +1)° + 2x O y = cx(x+1)¯³ – 2 II O y…

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

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