_x²+y? f (x,y) = e' 3 (sin(x²) + cos(y²)) %3D %3D 3

Q: find the integrating factor of cos(x)y'+sin (x)y=2cos^3(x)sin(x)-1

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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 – sin y) dx – (x cos y) dy = 0 -

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Q: Evaluate the double integral : (y³ – 12x) dx dy -

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Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

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Q: (b) Solve the integral [(3x – y)dx +(2x +3y)dy along the curve x = y' from (0,0) to (1, 1).

A: Solution of question as follows

Q: Compute the differential dy for y = (2x + sin x)². dy =

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Q: Obtain the general solution using separation of variables x cos² y dx + tan y dy= 0

A: Given differential equation is: x cos2y dx+tany dy=0 Apply variable separable: tanycos2ydy=-xdx…

Q: 11) (3ycos(3x)dx– sin(3x)dy)/ y = 0 12) sin(ß y)dx =-ß cos(B y)dy

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Q: 4. (y² cos x - 3x²y – 2x) dx + (2y sin x – x³ + Iny) dy when x = 0, y = e %3D 5. (x² – 1) dy = ((1 +…

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Q: (ylny-exy)dx + ( + xlny) dy = 0

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Q: Find the differential dy. x + 3 4x - 1 dy =

A: y=x+34x-1

Q: 3. The function 0(x) = 1/ sin(x) is an integrating factor of (ysin(x) + cos(x))dx + (x+ y) sin(x) dy…

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Q: 4. Find the double integration of [(1+xy* )dx dy. ww m

A: The given integral is ∫04∫y2y(1+xy2)dx dy

Q: 4. (y² cos x - 3x²y - 2x) dx + (2y sin x – x³ + Iny) dy = 0, when x = 0, y = e %3D

A: Note: According to our expert guidelines only one individual question is to be answered, kindly…

Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

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Q: find the integrating factor of the given linear DE and general solution of the y'+1/x (y)=cos(x)

A: Consider the given linear differential equation. y'+1xy=cosx The objective of the problem is to find…

Q: (1+x^2)+(y-e^ Arctan x)dx/dy

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Q: O1 Find: fx³ cos x dx using Integration by parts b. ſ cosx? 2x dx using Substitution Method a.

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Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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Q: 1. Solve for y of the Separable D.E. sinx dx +y dy = 0

A: To solve the given differential equation for y.

Q: 4. (y² cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e

A: exact differential equation

Q: Find the differential dy of y = tan x for x = π/4 and dx = −0.1.

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Q: Find the integrating factor: cos⁡ x dy+[(y sin⁡x )-1]dx=0

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

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Q: What is the integrating factor of the non- exact DE (4ху+ 3у?-х)dx+x\x+2y)dy %3D0 ?

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Q: zln x dx 2) S 3 cos3 x sinó x dx 3) 12.1 dt 13. 3t + 2

A: Explanation of the answer is as follows

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: Find complementary function and particular integral of d²y - y = xe* + cos² x dx2

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Q: - sin y, dz = cos x dx – cos y dy

A: Consider the given differential equation as, dydx=sinx-y

Q: Find the general solution of (cos cos y +ycos x ) dx + (sin sin x – x sin sin y ) dy = 0

A: The given differential equation is incorrect and hence the correct differential equation is as…

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: y² cos x - 3x3y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e x² - 1) dy = ((1 + x)2 -…

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Q: Intergrate dy (2y-x) =In Co)

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Q: dy of y = sin(3x² + 5x – 4) * In(e*) is dx

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Q: Evaluate the curve f(x, y) = 0 which passes through the point (0,4) and satisfies the differential…

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Q: Find the differential dy of the given function. y = x(1 − cos x)

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Q: the initial value DE y' - ytanx = sinx, y(0) = 1 cos 2x 5-cos 2x %3D 4 sin x 5-cos 3x 5-cos 2x В) у…

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Q: 4- Find dy/dx for y = 3[(sin-(e-3x*)1² dy 3(sin-(e-3*)1* In3 2(sin-'(e-3**) 1(-6x) %3D dx V1- e-6x2

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Q: 7. Given y = sinh(e* +tan (2x)-cos (x+1). Consider | dy (i) et 1 dx 1+e2x 1+4x 1-(x+1) dy (ii) ex 1…

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = arctan(x – 2) dy = ||

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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: 4- Find dy/dx for y = 3(sin-(e-3x²))2 dy 3[(sin-{(e-3*)i* In3 2(sin-1(e-3**) - 3x2 1(-6x) dx V1-…

A: Differentiate term by term

Q: dx o ex+x е. f. S sin(vE) dt S dx 2x cos(vE) dt COS g. dx 'x

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Q: Find the differential dy for the function y=3sin(2x)+x.

A: We have to find dy for the function y=3sin(2x)+x.

Q: dy - 1 = siny dx

A: Given : dydx-1=siny To Find : solution of Given DE

Q: Find the differential dy of the function y=(cos(x))(7x) a. dy=-7x(sin(7x))dx b. dy=(-cos(x))(7x)dx…

A: To Find the differential dy of the function y=(cos(x))(7x)

Q: 3) [ - cos dydx X X In 8 In y 4) S S e**y dxdy

A: (3) we have to evaluate ∫π2π∫0x21xcosyxdydx let  u =yx ⇒dudy=ddyyx         =1xddyy=1x⇒du = 1xdy…

Q: Find the differential dy of the x + 1 y = 4х — 5 dy =

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Q: (b) Solve the integral (3x– y)dx+(2x+3y)dy along the curve x = y' from (0,0) to (1, 1).

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