15. Evaluate the line integral J.(3xy* - 6xy ]dx + (4x°y³ - 3x?) dy, where C is any path from (1,2) to (2.1).

Q: Convert 1 √₁-x² √(1-x² - ₁₁² ₂ = ( x ² + 1 ² + 2 ² ) {/² e -x² -√√1-x² - y² dz dy dx in spherical.

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Q: 4. Evaluate fo (3x + y)dx + (2y – x)dy along the straight line joining (0, 1) to (2, 5).

A: We need to find the line integral ∫(0,1)(2,5)3x+ydx+2y-xdy .  We first parametrize the line segment…

Q: Evaluate xy dx + (x+ y)dy along the.curve y = 4x from (- 3,36) to (- 2,16). C xy dx + (x + y)dy =] C…

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Q: • Find so lutions usino Ex act Equations 1.) solve (ysinx t xycosx) dx + (Xsinx + 1)dy=0

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Q: Evaluate y = 4x 2 = [{(x² + 2y)dx + xy. dy} from 0(0, 0)to B(2, 4) along the curve

A: Given the integral is :                                  We have to evaluate the integral from…

Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

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Q: 6. Use Green's Theorem to evaluate O (y* – xy?) dæ + (2 – a*) dy where C is shown below. y -2 ² +y²…

A: Green's theorem

Q: Evaluate (2x - y) dx + (x + 3y) dy. JC C: x-axis from (0, 0) to (0, -3) and (0, -3) to (9, -3)

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Q: Evaluate the integral с by finding potential function. +2) ax + (x² + 3xy² + 2y)ay along any path…

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Q: Ev 2 x 2 [x²z dx - yx² dy + 2 dz along the curve C'shown in the figure. AZ 2

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Q: 2. Evatuate the following Complex Integration: 2-i (a) Evaluate | (3xy + iy?) dz along the straight…

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Q: Q.1 Put the D.E (x – 1)y" + 4.xy' + Ay =0 , in self-adjoin form .

A: If the diiferential equation is a0xd2yd2x+a1xdydx+a2xy=0 then its self-adjoin form will be…

Q: Classify each of the following equations as to order and degree: a. 3dy + (4xy - secx) dx = 0 b. L…

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Q: 2. Evatuate the following Complex Integration: 2-i (a) Evaluate | (3xy + iy?) dz along the straight…

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Q: 24. Show that Legendre's equation (1-x²)y" - 2xy' - λy=0 is self-adjoint.

A: A differential operator L[Y]= p(x)y" + q(x)y' + r(x)y = 0  is said to be self adjoint  if its…

Q: The linear DE (2xy + x² + x²) dx-(1+x²) dy=0 when reduced to standard form yields -2x 1+x² dy x² C.…

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