Q₁: solve the following differential equati a) xy' y = x + 2 y ² 4 the to b) (x+y) dx - xdy = o 1 0 C) (X-1)³ + 4 (X-1)² Y = X+1 dy dx d) cos y dx + (x siny - cos²y) dy = 0 e) x²³ cos y - x + 2 dx dy = 0 f) (9²-4) (x-1) = (x+)) dx dy д) у g) y' ex+y = cosh x + √cosh³x -1 +7 e* h)(3x y + 4y) dx + (3 x²y² + 2x) dy= = 0 Isin x dy SIX-Y COS X (1-9²) dx + (1+x¹) dy = 0 (2) 2x² dy csc(X) dx M) Ý xẻ vxz

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: Q1) Solve 1 + cos y – 2xy) dx – (xsin y + x²)dy = 0 +1

A: Given differential equation is  1x2+1+cosy-2xydx-xsiny+x2dy=0 This equation can be written as…

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: x*y"+xy'+(x? y=x cos x 2. Show that is a solution of the equation

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Q: гуг 0 = fp ( ²4 2² - 62²) + xp (T-H10

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (6) [²/2 sin² (2) cos2 (x).dx = A) 플 B) 플 C) 미플

A: We need to make it proper to solve this integration.

Q: What is the derivative of y = sin (x³ sin (x³ – 3x)?

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Q: (1) (II) 10 F. 10 +t 10 10 -10 -10 (II) (IV) 10 10 斗t 10 t 10 -10 -10 a) y = 10e-t/2 cos 2nt b) y =…

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Q: JO (5) Find the derivatives (a) d # t ( * cos(2³) dz + 35e) 4

A: Since you have posted multiple questions i can do first question as per our company guidelines.…

Q: Solve 3e* tan y dx+(1-e*)sec² y dy = 0.

A: To solve the given differenrial equation.

Q: Let y -2 = S sin³ (t) dt. Use the Fundamental Theorem of Calculus to find y'. ex

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Q: Q4 B) Find y' for the functions cos(xy) + 3*+cos ly+ In(xy) + log-7 dy

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Q: dy cos?x = -(tan x)y ;y(0) = -1 b) Solve %3D dx

A: Given that: dydx-cos2x=-(tanx)y; y(0)=-1

Q: a) 12 Q.7) To write the power series £=3 4m as the form -4m a) m - 1 we must shift m to become : d)…

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Q: Using Variation of Parameters 4y''-4=cos-1x

A: Given that, 4y''-4=cos-1x Now let's take, 4y''-4=0 Take m=ddx, 4m2-4y=04m2-4=0m=±1 So the homogenous…

Q: y = Vr² + VT etin e y = r-5 y = (cos z)n. y = /tan 2x – sec3 (4x – 1)

A: as we are just given 4 functions and not any question so I assume we need to find the derivative of…

Q: Q.1) The general solution of the equation e' cos , is:

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Q: Solve

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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: (a) a²y + y sin r = xy. (b) y = x³y - 2y³. (c) y = e²-2y (d) y'= x² + y² xy

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Q: Determine the general solution: (dx/dt)A3 - (dx/dt)^2 - 4x = 0 Select the correct response: O y= c1…

A: Topic:- differential equations

Q: (2 sin(y)) dx + (x y cos(y²)) d y = 0

A: Variable separable differential equation

Q: c) y(x) = c, + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is…

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Q: (2,–2), (4,4), (5,3) by a CUDIC SPime. 4. Determine constants a, b, c, d and e that will produce a…

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Q: 3 x* cos(3 y) 2 x³ sin(3 y) dx + + 2 x2 ) dy = 0

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Q: If y(t) is the general solution for the equation: y' + y = sin(t), y(pi/2) = 0 Then, y(0) = ? a)…

A: Consider the differential equation  y'+y=sint,           yπ2 = 0

Q: Show that y sin x is a solution to xy" + (2 secx)y' + xy = 2. =

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Q: Solve the D. E. to the I. V. P. sinx(e¬ + 1)x' – cosx = 1, y(곡) = 0 - O (1 + e') (1 + cos x) = -1 O…

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Q: An environmental engineer wants to evaluate three different methods for disposing of nonhazardous…

A: GIVEN