Solve the following DE: [3sin (y) — 5x ]dx + 2x²cot(y) dy=0 Ox²[sin (y) - 2x]³=C'sin³(y) Oy³[sin(y) +x]²=Csin³(y) Oy³[sin(y) + x²]²=Csin(y) Ox³[sin(y)-x]²=Csin²(y)

Q: Find g'(x) if g(x) = t² cos 6t dt %3D 2

A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

Q: 5 Find y' if cos (Xty) =

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Q: Q3) Simplify (if necessary) then Compute: y"+ 2y Where y(x) = (zx+ cosx*)] [4(cosh2x-sinh2x)] d 2,2…

A: To find -  Simplify (if necessary) then Compute : y'' + 2y' where yx = ∂2∂x ∂zz2x + cosx44cosh2x -…

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: 1. Find dy/dx a) y = In (2x² – 3x) %3D b) y = [e" dt ) d) y = In|sec(x)+ tan(x) e) y = 7std*) S)y =…

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Q: 4. Calculate zu for z = 2x-y x+3y x = e2u cos(3v), y = e2usin(3v) "

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Q: Directions: Choose the letter of the correct answer. Write the letter that corresponds to the…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 2. Solve 3 y'(z) + y(x) = y²(z) (cosz - sinx)

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Q: 3. Integrate the function. (a) / Vx–1dx = %3D (b) /e2+ 2x+1 dx = (c) | (sin xcosx+ sinx cos x) dx =…

A: Hello there! You seem to have uploaded a question with multiple subparts. As per our guidelines, we…

Q: cos(x) * еУ + 9у %3D Зу8 — 5х + 10е =

A: The expression cos(x)×ey+9y=3y8-5x+10e. We have to find y' or dydx.

Q: (i). y' = 1 + 3y tanx Ans. 3y cos³x = c + 3sinx - sin³x

A: this is a linear differential equation. solve it using integrating factors.

Q: Find dy/dx if y= cos-1 In(x+1)

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Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. (A) cos y sin x =C sin y B…

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Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: (ii) y = e2x cos(1+2x²) (1+2x²)

A: y=e2xcos1+2x21+2x2

Q: Integrate e* cos(x) dr COS

A: To evaluate: ∫02πexcosxdx To solve this we will use integration by parts

Q: (1+x)y' + y = cosx; y(0) = 1

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Q: find dy/dx of the following:

A: Please refer to the image below

Q: 4. Find d²y/dx² for the following functions: a) y = sin x? cos 2x

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Q: 2/x?y" – 2xy' + 2y = x³ cos x

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Q: - (2xy - sin x) dx + (x² − cos y) dy = 0

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Q: if  x²v+sin(xu)-yv²+u³v=1 x²u-2yv=1 ، cos(xu)+yv=5  ,find dy/dx

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Q: (a) (b) y' = 2y + t²e²t ty' + 2y = sin(t)

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