(ey – y cos xy)dx + (2xey – x cos xy + 2y)dy = 0

Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e %3D 5. (x2 - 1) dy =…

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Q: [2x + y cos(xy)]dx + [2y + x cos(xy)]dy

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Q: dy (e2y – y) cos x = e'sin 2x, y(0) = 0 = dx

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Q: (e* sin y – 2y sin x)dx + (e* cosy + 2 cos x)dy = 0

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Q: (e – y cos (x)) dx + (2xes (ey – y (xy) + 2y) dy x Cos cos = 0 3.

A: Exact differential equations

Q: 2x + y cos (xy)] dx + xcos ( xy) dy = 0

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Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

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Q: z= cos y Using the substitutions the DE (3cos y - 5x) dx – 2x?tan y dy=0 reduces to dz= - sin y dy

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Q: x'e* cos 3xdx + -dy = 0 Vỹ - 1 %3D

A: In this question, we solve the separable differential equation by direct integral. the differential…

Q: dy Find the particular solution of 2y- = x+ sin a when y (0) = 1

A: we have to integrate both side , we get

Q: y= A cos at a solution to y" + 3y = 0 such that y' (1) = 2? %3D

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Q: e2 (2 cos y dx – sin y dy) = 0, y(0) = 0 – sin y dy) = 0, У (0) %3D

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Q: 2. a“y dx2 dy + 42+ 3y = sin(x) + 2 cos(x) dx

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Q: d = cos(zx); y(0)=1 dx %3D a. y=sin(x) b. y=cos(zx) sin (x) C. y= 1 d. y=-sin(x)+1

A: Given, an initial value problem we need to calculate the solution:

Q: {[1+ y?] sin(xy) + xycos(xy)}dx + {[1+x²] cos(xy) – xysin(xy)}dy=0

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Q: (sin(æ) + 2 cos(y)) dy ^ dz + (zổ – y cos(x)) dz A dæ + 11xyz dx ^ dy. Find dw. dw dx ^ dy ^ dz

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Q: 3y" (t) – / (t) = e' cos(t) + sin(t), y(0) = 0, y'(0) = 0 -

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Q: COS f(2, Y) af af dy f(x, y) = log, (3x) af %3D fe dy

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Q: 2(x + y)dx – x(x + 2y – 2)dy = 0 ? cos y et 1+x² O D y2 e`y O A B

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Q: B. (y + e*seny)x + (x + e*cosy)dy = 0

A: The differential equation is given as  y+exsinydx+x+excosydy=0 Compare it with Mdx+Ndy=0 to obtain…

Q: (x – y* + y? sin )dx - (3xy + 2y cos r)dy subject to initial condition y(0) = 1 (M

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Q: If y = x* cos' x-e* In( 7x +1) , then find dy at x=0. dx 3

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Q: - d² y dt² y (0) = 10 dy 4 - 5y = e-3t sin(4t); y (0) = 3, dt

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Q: (y − cos²x) dx + cos x dy = 0

A: To solve the differential equation: y-cos2 xdx + cos x dy=0 Let us simplify this, y-cos2 xdx + cos x…

Q: g) y² ex+y = cosh x + √rosh²x -1 +7 et h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy Sin 2x…

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Q: dx y of y = cos 1 (In (xy)) Find %3D CoS dy

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Q: 1 - (хdy— ydx)%3D0 а. x²+ vz (xdy-ydx)= 0 b. 1 (x² – y2] V<dx+x²dy)=0 С. у' + y tanx %3D secx + cosx…

A: Given,

Q: e^(x)cos(y)=1+sin(xy) dy/dx?

A: To differentiate :

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: Find the General Solution dy = y2 – 3y?cos (x) dx 1. dy (x² – 1) = 2xy 2. dx cot x dx +y sin? x dy =…

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Q: {[1+ y²] sin(xy) + xycos(xy)}dx + {[1+x²]cos(xy) – xysin(xy)}dy=D0

A: Given     1+y2sin(xy)+xycos(xy)dx +1+x2cos(xy) - xysin(xy)dy=0

Q: b) Differentiate y = e (In3x) + tan (3y) with respect to x. %3D + 2e In 3x Ans: dy %3D 3 1-

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Q: dx + 3x dt cos(5t) %3D with x(0) = 1. x(t) = %3D

A: The given initial value problem is: dxdt+3x=cos(5t) ;         x(0)=1

Q: Given that y + x + cos(xy) = 0. Show that dy/dx = ysin(xy)-1 /1-xsin(xy)

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Q: (xy cos.xy +sin xy)dx +(x² cos.xy +e' )dy=0.

A: We have to solve given problem:

Q: 25. (y cos x + (2y sen x – xr + In y) dy = 0, y(0) = e 3xy – 2x) dx –

A: The given differential equation is: y2 cos x - 3x2y - 2xdx+2y sen x - x3 + ln ydy=0  ;…

Q: (у — сos*x)dx + cos x dy %3D 0

A: We need to find the solution of y-cos2xdx+cos x dy=0 This differential equation can be written as:…

Q: Find the differential dy of the function y Provide your answer below: dy= dx = 5x4 + 4 4x + 3

A: y=5x4+44x+3Differentiate w.r.t xdydx=4x+320x3-5x4+444x+32

Q: (e* – sin y) dx + cos y dy = 0; when x = 0,y = 1 - %3D

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Q: 30. cos(r + y?) dx dy 32. x²+ y² dx dy 2 y

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Q: • T/4 cos(0) f |/| f(x, y, z) dV = 9p sin(ø) cos(4) dp d0 dø, find f(x, y, z). E f(x, y, z) =|| ?

A: We have to given ∫∫∫Efx,y,zdV=∫0π2∫0π4∫0cosθ9ρ2sinϕcosϕdρ dθ dϕ Now the function which is to be…

Q: Scy dx –x dy; C is the cardioid r=1- cos 0.

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Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: x dx - Ja- x dy = 2. [2x +y cos(xy +xco6(xy)dy = 0 1.

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Q: Hw #4 ( 2 xy +y -tany) dx+(x²-x tany tSeiy )dy =o ??

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: 5. (e* – sin y)dx + cos y dy = 0; when x 0,y = 1/2

A: First we will convert the given differential equation into linear differential equation by…

Q: 3. Find dy, where; (x+y) = 2 a) cos (xy)- + e b) e+ iPtany=1 , u= xlax (use chain rule)

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Q: dx 2- Find dy of y = /cos-1(In (xy)) y %3D

A: Given: - The function is, y=cos-1(ln(xy))xy To find: - The derivative of the function, dxdy

Q: (у — сos-x)dx + cos x dy %3D 0

A: The given equation is y-cos2xdx+cosx dy=0 rewrite it as y-cos2x+cosx…