28. (ху? + х — 2у + 3) dx + x*у dy 3 2(х + у) dy; when x — :1, у %3D 1. ANS. (ху — 2)?+ (x + 3)2 — 2у? + 15.

Q: 4. (у- 2ку + 6x) dx - (x?- 2ху + 2) dy -0

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Q: Equations). =x (1 – y²) 2 + 5y + 2x + 10 2ху — 10у — х +5 -dx + -dy 2х + 3 у — 6

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A: The given differential equation is y e2x dx=4+e2xdy Solving the differential equation by converting…

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Q: 4. Homogeneous: Solve the equations (x – y) dx + (3x + y) dy = 0; when x = 3, y = -2

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Q: 1. у%3D х3 — 2x2 + 3х — 5 y = 3 — 2х2 + 3х — 5 dy — Зx2 — 4х + 3 dx

A: Given: y=x3-2x2+3x-5

Q: Consider %3D S"+\S=0

A: Given,                           S''+λS=0                        ...(1)and…

Q: 0.7.8: Solve: dA HP а) = -10A, A(0) = 5 b) 3 ЗН, Н(0) 3 1 dt dx d²y с) = 4y, y(0) = 0, y'(0) = 1 dx2…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

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Q: Find the general solution for (3/y-6/x)dx - (3x/y^2 - 7/y)dy

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Q: 7.5- yy - 9 4+9) dy -6- 8.S 1 dx e2x+ e-2x

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Q: Prove that A → B = (Vx)A B- (Vx)A → (Vy)B, if y is not free in B.

A: To prove that A→B ↦∀x∀A→∀yB, if y is not free in B.

Q: 2. 3t3 dx = x(x²+ 212) dt. Solve by two methods. %3D

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Q: Eulers method- dy -u メーツ dx X+4 y(6)=1

A: Euler's method states that  yn+1=yn+h·f(xn,yn)...(1) where, xn+1=xn+h

Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

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Q: Evaluate the definite integral using the given values

A: Given that ∫26x3dx=320,    ∫26xdx=16,   ∫26dx=4. Consider the integral ∫262x3-10x+7dx. Evaluate as…

Q: The displacement of an object is given by the parametic equations:  x=0.2t^2+2t and y= -0.4t^3…

A: The displacement of object is given as, x = 0.2 t2+2t   andy = -0.4 t3   we need to find the…

Q: dz (D² + 16)*(D² + 4D – 5) (D² + 2D – 3)*z = 0, Dz = dx -

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Q: general solution of (2xy³-2x³y³-4xy²+2x)dx+(3x²y²+4y)dy=0

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Q: Solve: 0 < 5x + 5 < 4 The answer has form: A < x < B Where A = Preview and B = Preview Box 1: Enter…

A:

Q: Exact method 1- (6x2 + 4xy +y²)dx + (2x² + 2xy-3y2)dy = 0

A: Exact differential equation

Q: у (2ху+1) dz +a (1+2ху— г3 у?) dy 3 0 (1+ 2гу— а* у) dy %3D0

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Q: y = (2x2 + cotx)³ P a. y' = 3(2x² + cot(x))² (4x – csc²(x O b. y' = 3(2x2 + cot(x))² (4x – cot?(x) P…

A: Given query is to find the derivative of the expression.

Q: 4- y 2- 2 10 12 -2- -4 -6 2 (a) f (x) dx = Number (b) f (x) dx dæ %3D Number 6J

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Q: 2. (бх * у) dx +у (2х - Зу) dy 3 0

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Q: dy B) dz3 -6 dy dy + I - dz

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Q: (2х + Зу — 5)dx+ (3х — у — 2)dy %3D0

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Q: 2. x =1+y², x = 0, y = 1, y = 2 about the x – axis.

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Q: Assume that a factory can produce a quantity 2x3 + x°y + y4 of goods, when x is skilled workers, and…

A: Here we use the concept of implicit differentiation.

Q: 1.) y = ,"(x* + )d. 3 1.) у 3 /1-х2, 2.) у %3D S Vu du

A: Newton-Leibnitz rule :                ddt∫g(t)h(t)f(x)dx=f(h(t) dh(t)dt   + f(g(t) dg(t)dt Note…

Q: 2 (4-х2 2 The integral LG. -(x² + y² ) dzdxdy is Vx² +y? -2 J-/4- 2 C[* dzdrdo .3 dzdrd0 2 •T/2 2 p³…

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Q: (2, 3), dy If x2 + xy = # = 10, then at the point dx

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Q: (2x-3y+6)dx-(4x-6y+2)dy=0 in Linear two variables with POI

A: Here, the given differential equation is: (2x-3y+6)dx-(4x-6y+2)dy=0 The equation can be written as:…

Q: Find Wer if W = f(x,y) [x = rcost, y = rsint

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Q: Transforming - Ⓒ S 1 = ²2²1dz 1+z² ℗ B / 1 + 2/2 d -dz 1-z² Ⓒ *2-2z² 1+z² (A) dx secx + C-²₁- -dz…

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Q: Stue; dy = (1-x)y²+ (2x-Dy-x given Sdutfon y-1 %3D

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Q: 22 32 S[ (4-y ) dydx 1. ans:- 3 0 0

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Q: x2 -dx 1+ x4 -dx (x² + 1)²(x² + 2.x + 2) 1 -dt, for a> |6|. > [b]. а a +bsent

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Q: {6} = I ( (b) T = [4,9) %3D (c) T = [-4,9] -

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Q: y (+zy'+y= ctDsint %3D

A: Given an ordinary non- homogenous differential equation : y(4)+2y'+y=(t+1)sint We need to find the…

Q: 2A T -t + A, 2A --t + A, T -T t≤c 2 T 0 Osts 1/2

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Q: If y(#) = and z increases from 0 to 0.5 then dy = 0.5. %3D %3D 1+ *

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Q: ^4-x² •6-z 2. Evaluate: dy dz dx. 3x2 4-z 3. Evaluate: dx dy dz. Jo Jo 0.

A: To solve the given triple integrals

Q: (x+2y-1)dx+(5-2x-y)dy=0; y(0)=0, implicit solution  Also: a) Value of y if x=2

A: By arranging the question and then taking boldfaced ratio we'll get the answer. Here,I am providing…

Q: (х+2у -1) dx - (2x+4 у-3) dy%3D0

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Q: The Method of Variation of Parameters (3) y" + 4y = sec x

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Q: 4. 2(2ху + 4y — 3)dx + (x + 2)*dy %3D0 (Non-exact)

A: The solution for the asked part is given as

Q: 3.2.2 Test for exactness then solve. y(2xy2 − 3)dx

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Q: dy х+2у-3 dx 2х+у-3 (2х + 3у)dx %3D (у — х)dy %3D0

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Q: Find the General Solution 1. 2(2xy + 4y -3)dx + (x+2)2dy=0

A: 1) 2(2xy + 4y -3)dx + (x+2)2dy=0 Repost the next parts.