dy dx 4. sec? y +2x tan y =x III. Solve each of the following: 1. (3x +y -8)dx + (x - 2y + 2)dy =0 | 2. (16x + 5y -6)dx + (3x +y-1)dy = 0 V 3. (x - y - 2)dx + (3x +y- 10)dy = 0 (2x +3y + 3)dx + (3x - 4y +13)gdy = 0 5. (3x +y - 9)dx + (x – 4)dy = 0 4.

Q: Find y (2) if D.E. 2 dx +3y=sin 2x₁ y(0) = 6

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Q: 14 نقطة Q) Find dy/dx of the following * :equation (x² +x)(x' - x +1) y: dy/dx = -3/x^4 O %3D dy/dx…

A: Given y = x2+xx2-x+1x3y = x4-x3+x2+x3-x2+xx3y = x4+xx3y= x+1x2

Q: d²y Find С. dx? 1. y= sin 2x +cos² x sin x 2. у- - y= 1-cosx

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Q: 5. Solve d²y dy dx² dx +2 + 5y = sin 2x, given that y(0)=3, y'(0)=0.

A:

Q: 4- Find dy/dx for: a- y = sec?x – tan²x b- y = sec (– x) c- y = sin(tan(3x))

A: As per our guidelines ,we can solve only first 2 subparts of a question.Please resubmit the other…

Q: 4. Substitution Suggested by the Equation: (x+2y-1)dx+(x+2y)dy = 0

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Q: Solve the following exact equations: 1) (сos 2y — 3x*y*dx + (сos2y — 2xsin 2y -2x'y)dy %3Dо 2) (2ху-…

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Q: Find the particular solution of csc y dx + sec2 x dy = 0; y = π/2 when x = π/2

A: We solve this differential equation by separation of variables.

Q: The solution of (1 – y² )dx + (1 + x² )dy = 0 is: tan x = c + tanh¬' y = c Option 3 an-'(v/x) = c…

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Q: Solve for the given DE: y(y^3-x)dx+x(y^3+x)dy=0

A: first we will check this is exact or not this is not exact then we will find its integrating factor…

Q: dy d²y B) Find if x = sin² 3z and y = tan 3z and dx dx2

A: We differentiate the function.

Q: dy 2y ! = -x² y² sec²x %3D dx +

A: Using solution of Bernoulli Differential equation.

Q: y tan x dx + In* ydy=0

A:

Q: The solution of (1 – y² )dx + (1+ x² )dy = 0 is: tanx =c tan-x = c + tanh¯y=c Option 2 O Option 3…

A: Basic :-1 ddx tan-1x = 11+x2 ⇒ ∫11+x2 dx=tan-1x+c2 ddx tan h-1y = 11-y2 ⇒ ∫11-y2 dy=tan h-1y+c

Q: dy Find dx 3 (a) y = (3x² – 4x + 5)° (b) y = Vsin x + cos x (c) y = 2e¤²+5 cos (e2")

A: (a) To find: The derivative of y=3x2-4x+53. Concept used: Chain rule of derivative: fgx'=f'gx·g'x…

Q: Obtain the general solution to the equation. dy 1. y + 2x + 1 dx

A: Given that: dydx=yx+2x+1

Q: c) Obtain a general solution of + ! dy dx Y = sin x.

A:

Q: 4 Find dy/dx for: y = sec?x- tan²x b- y = sec -x) C- y = sin(tan(3x))

A: It is asked to differentiate the following functions with respect to x: a) y=sec2x-tan2x b)…

Q: Q-2) Solve: d²y + 2- 8y = 0 dy dx2 dx Where y (0) =1; 2 dy (0) =8 dx

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Q: G. Substitution Suggested by the Equation 1. (2x – y + 1)dx – 3(2x – y)dy = 0 | 2. (3 +x cos y)dx –…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: (b) (x² + xy) = y² y = 1 when x = 2 dx dy (c) - y = e* sin(2x) y = 1 when x = 0 |

A: Given : (b)  x2+xy dydx=y2  ,         y = 1 when x = 2   which is y2=1 (c)   dydx-y= ex sin2x ,…

Q: Solve Hhe dipperential Eguentione. 3(x+zy-4) dy + Gx-3y +2) dx= 0

A: Wea will convert the equation into homogeneous differential equation by substituting and then solve…

Q: 1. Solve the equation 3(y+1)dx-(x+y+3)dy =0.

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Q: Solve the equation (4y + 2x – 5 dx + (6 y + 4x – 1 dy = 0 subject to the initial condition y(-1)= 2.…

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Q: Find the solution of the equation a²z a²z + cos y V ax² dy² which tends to zero as x→∞ and has the…

A:

Q: Can you help me step by step?

A: The derivative of a function is computed as follows.

Q: solve the di¡erential equation.3. sec x dy + x cos^2 y dx = 0        4. 2x2 dx - 3sqrt(y) csc x dy =…

A: 3).To solve the differential equation: secx dy+xcos2y dx=0. Solution: Separating the variables of…

Q: 2. fG-4) dy (у— 4) 5 (y+3)* 4 4. [(e* +e² )*e®x-2) dx 5. ſcsc'(2x)dx 6. (1-3 tan ysec y)'dy 7.…

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Q: I. Find the general solution of the following: 2 dy = -2x + 3x -2x = 3e dx (x²+5)dx- (2y - 1)dy = 0…

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Q: - 2y 4 given that y = 3 and 4 when x = 0. Solve dx2 %3D %3D dx

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Q: B. Substitution as suggested by the equation 3. (x + 2y – 1)dx + 3(x+ 2y)dy = 0 when y(0) 4.…

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Q: Solve the Bernoulli's equation dy/dx −1/2(1+ 1/ x)y = (3 /x)y^3

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Q: Find the solution. dy X-+ 2y = dx sin x y(2) = 1 A cy = (3 – cos 2x – tanx)/x? B x = (2 + cor2 –…

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Q: Find the solution y = y(x) of dy y2 +y dx 0, x3/2 subject to y(1) = 1.

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Q: d?y + 16y= 10 cos 4x dx2 Solve given y=3 and dy =4 when x=0. dx

A: Given: d2ydx2+16y=10cos4x So, we can also write as: D2+16y=0 The auxiliary equation is: m2+16=0

Q: 1. y(4x+ y)dx- 2(x² – y kdy = 0 | 2. 2xydx + (y -x² kdy = 0; when x = 2 and y = 1

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Q: 8. Find cyldx of the given equation: x²y- y'x 4 a. dy -2xy-y x+2xy dy dx x+y 1. dx dy dx x2 +2xy +y?…

A: To find dydx of the equation x2y-y2x=-4. Solution: Power rule of differentiation states that:…

Q: Solve the DE. (1+x²)dy + [(1-x)²-xe^-x]dx = 0; when x = 0, y = −2

A: This is a problem of ordinary differential equation. first of all we will simplify it into dy/dx…

Q: Н.W. Solve 1- xdy – 3ydx = x*y-!dx 2- (2xy2 – 2y)dx + (3x²y – 4x)dy = 0 3- [y?(x + 1) + y]dx + [2xy…

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

Q: Q4) find 2 for : dx y = sin(x") + 2* +n

A: Use simple formula of derivative

Q: 2. Find the solution (implicit or explicit) dy (y+1) = 3sin(x). y(7)= 2 dx %3D

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Q: Solve the following dy 1. xy dx = 2y2 - x2 %3D | dy 2. x2 dx xy = (x² + y²) tan-() (x + y2) tan-1 dy…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Obtain a solution to this linear equation. dx − (1 + 2x tan y) dy = 0

A: Given that: dx − (1 + 2x tan y) dy = 0

Q: - +5. dx + 6y = 12(x+e") 1 dy given that y =- and = 3 when x

A:

Q: 16. (12x2 - 10ху +2у' +4) dx +(бху? - 5x3) dy %3D0 18. (tan y+ ycos.x)dx+( senx+x sec² y)dy = 0

A: Follow next step

Q: find explicit solution: x^2 dy/dx =y-xy       y(-1)=-4

A: Given differential equation is                                       here we can easily separate the…

Q: [2x + y cos (xy)] dx + x cos (xy) dy = 0 solve for the particular solution using x = 1, y = 1/2 %3D

A: we have to solve the differential equation

Q: 1. Find the solution of dy xy %3D dx (1+x)(1+y)

A: The given problem is to solve the given ordinary differential equation. Given differential equation…

Q: Find the general solution of a) (2wv- tan w) dv + (v^2 - v sec^2 w) dw = 0

A: (a) The differential equation is given as (2wv-tan w)dv+(v2-v sec2w)dw = 0 Compare it with Mdv+Ndw=0…