%3D iv) if zy = (x)- then zz + Zy = %3D 2

Q: II. Coefficients Linear in Two Variables 1. (6x-3y+2)dx-(2x-y-1)dy=0 2. (9x-4y+4)dx-(2x-y+1)dy=0

A: We can solve the given differential equation.

Q: Find the solution of the homogenous equation: 2(2x2+y2)dx-xydy=0

A: The given differential equation is  2(2x2+y2)dx -xy dy=0

Q: С 20 3x-1 хр. -X (3+3 (2) j² dx a Лх lo XS хр sự X Сў-12.d:

A:

Q: fx=å (3in (x*ry)-x2) %3D fy = Ly(31n (x*+y)-x2) %3D d fe-(3in (x*ry)-x2)

A:

Q: 2. Using the variation of parameters, find the particular solution of (D² + 1)y = sec x

A: By the method of Variation of perameters

Q: Find positive numbers x and y satisfying the equation xy=20 such that the sum 4x+y is as small as…

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Q: y'" — 7y' — бу = 0

A: Solution :- This higher order differential equation can be solved simply by using complementary…

Q: 2 dy U=x-4 Eilsy =4-24 ذا كانت %3D

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Q: sheet Undetermind Coefficient 2 Y +2Y+Y=x'e хе

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Q: x²+1 If A = S* S dx, then A– x = %3D x²-4

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Q: 6 - 3x2 + 3 Find the general antiderivative of f(x) - - - x5 + C

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Q: (b) Use Gaussian elimination to find the values of x, y and z: x+2y+3z=10 -x+y+z=0 y=z=1

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Q: Find the values of ∂z/∂x and ∂z/∂y at the points xey + yez + 2 ln x - 2 - 3 ln 2 = 0, (1, ln 2, ln…

A: Given that, xey+yez+2lnx-2-3ln2=0          ...(1)

Q: E (X² + Y²) E (XY)

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Q: 4) f(x, y,z) = /1– x² – y² – z²

A: Domain is the subset of R3 where the function is defined

Q: %3D iv) if zy = (x)-1 then zx + Zy = h.x + y c.-z (x + y) d. z² (x – y)

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Q: f(x) %3D e 3.

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Q: (2xy + 3x²)e, + (x² – 2yz + 2y)e,- (e2 +y²)e, olan f(x,y,z)

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Q: t sect df 2/ V3

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Q: x+x-2 dx If S (x²–1)(2x-x²) dx can be resolved into A S+ Bƒ f(x)dx + D ƒ g(x)dx , then

A: Using partial fraction to solve the problem.

Q: Find the solution. 1. ху3dх + (у + 1)e-*dy — 0

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Q: 2. y" – 2y' – 3y = e²", y(0) = 1, y (0) = 0, Yp(t) = -e2' /3 %3D

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Q: 8.s Y°+y² _ dy + y² – 1 y2 + 1 8. S

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Q: y" - y' - 2y= e* %3D

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Q: y' +(E- 1)y ==

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Q: (xi+axy-3)dk + 2x°dy -0 3)ck +2x²dy =0 Qxt -3x*y? +x = 3 +2xy -3n =0 O Option 3 O Option 1 x+ 6x…

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Q: %3D iv) if zy = (x)-1 then z, + Zy = b.x+y c.-z (x+ y) d.z² (x- y) a.x-y

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Q: af If 2xy(-x² + y) + xe", what is ду ду? Select one: а. 4ху — 2x3 + хеУ ду? 2x(-x² + 1) + xe" b. ду?…

A: Given ∂f∂y=2xy−x2+y+xey

Q: 2. Find the solution of 2x³y' = y (3x*+y?). Use Integrating Factors Found by Inspection.

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Q: solution of the di dy x + 4y = * x2

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Q: y"+ 4y = x What is the particular solution y.? Yp

A: helar we have to find particular solution of the given differential equation. the solution is…

Q: y fa(4y) -1.0 -2 1/8 -0.5 -1 1/4 1/2 1/8 0.5 1 1.0 2 Find the E (X), E(Y), V (X), and V (Y). 2.

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Q: e solution of the di: 0.1 with step size 0

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Q: 3(1 + P) = 2ty(y³ – 1) dt %3D

A: Let us consider the differential equation dydt+P(x)y=Q(x)yn It is known as Bernoulli's equation…

Q: S(x)=-2x+8x S(3) = %3D S(-1) =

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Q: 1 Q4- If you have 1 then x ... And y = %3D x+iy 1+2i

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Q: Зх-1 4x+2' , find a) R , and b) R(x+h)-R(x) x+2, 3. Given R(x) = E) %3D

A: Given: R(x)=3x-14x+2

Q: If y = Eo(k + 1)z*+3 then y' = .

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Q: Í (x)dx, iff(x) = Vx -k +1;k-15x <k, k = 1, 2,.n.

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Q: Specifically a differential equations problem. Question in pic below.

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Q: X1 + 2x2 – x3 = 3 5x1 – 2x2 = 2 -3x2+7x3% = 2 %3D e for the y's

A: Given,          0x1-3x2+7x3=2          x1+2x2-x3=3          5x1-2x2+0x3=2D=0-3712-15-200-3125-2=-69

Q: A particular solution of y -2y + y e':

A: Given differential equation:     y'' - 2y' +y = et We use method of undetermined coefficient to…

Q: (a) In e7 (b) eln 2 %3D (c) eln v3 %3D Preview (d) In e5

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Q: f Lan 2X e *3 of +sec2X Pinel dy o

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Q: (ii) y" – 4y' + 4y = e3", y(0) = 0, y'(0) = 0. %3D

A: We have to find general solution of the given initial value problem.

Q: , у"+ бу'+ 9у 3D 0; x = 0, y = 0 and x = 0, y' = 3 = Ans. y=3 x e-3*

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Q: Solue %3D ylo). ! y'co)> -2

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Q: 5. y = xArctanx - In V1+x 6. y = In (e* + e*)

A: topic-second derivative of a function