(5) (sec-i x) =, d

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: sec( c)+y dy e sec do

A: Given differential equation is homogeneous equation

Q: 18y sin3 9y2. 10) +3 cos V9y2 + 3 dy + 3 cos

A: See the attachment

Q: Find the anti-derivatives, using ONLY basic rules + 3* ) dx

A: Note:- We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: [11 sec²(x) dx convergent divergent

A: We have to check that given integral is convergent or not.

Q: 5z² – VE 1+ tan(x) Find an dy when y = dr Do NOT simplify. expression for

A:

Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

A:

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

A: To solve the given differenrial equation.

Q: - sinx) dx 2. 1. (COSX (ax' +b)*x dx 2. 2/3

A:

Q: Show that : y' = 1 when y(x) = sin-(x) %3D V1– x2

A: Differentiation is done in many ways. Some of the rules of differentiation are illustrated below :…

Q: tanx dx = -In/secx|+C^O .BO In|secx|+CO In/cscx| +CO -In|cscx|+C°O .D

A: We need to evaluate the following integral I = ∫tanxdx

Q: | cos 3y dy 4.

A: I=∫ cos6(3y) dy3y=tdy=t3Integration by parts;∫uv dx=u∫v dx -∫ dudx ∫vdx dxI=13 ∫ cos6t…

Q: (cos 2y-3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0

A: Given : Differential equation cos 2y - 3x2y2dx + cos 2y - 2x sin 2y - 2x3ydy = 0   To find :…

Q: tan (2x + 3). Find the differential dy when x = 3 and dx Let y = Find the differential dy when 3 and…

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Q: 4. FIND d²y BY IMPLICIT DIFFERENTIATION: x² + y² = 81 %3D dx2

A: Given: x2+y2=81

Q: in integrating the function fx cos() dx using intogration by parts, whut would you choose for your…

A: Solution

Q: Find dy/dx at the given point. 7x2y4=9-x2-9y  at (0,1)

A: Given: 7x2y4=9-x2-9y We have to find the dydx at (0,1)

Q: 3. f(x,y) tanx - sec²x - cosy

A:

Q: find dy/dx

A: y=∫sec x21t2+1dt.

Q: 2 In sec Vi + tag V + C sec sec z dz %D

A: 35. given integral,∫sec x . dxx = 2∫sec x12 . 12x-12dxlet x12 = u⇒ 12x12-1 dx = du⇒12x-12dx = du

Q: - ((x3 + x)sech(In x)) = dx EX)-

A: To find  ddx(x3+x)(sech(ln x) We use product rule  d(uv)=udv+vdu Let  u=x3+x,     v=sech(ln…

Q: 10. J(3x3 — 5х + sin3x) dx -

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Q: The integrating factor of Y + 3y cscx= cotx is?

A: Consider the given differential equation, y'+3ycscx=cotx This is the first order linear differential…

Q: 7. 2r tan y dx + sec² y dy = 0

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Q: (3+y +2y² sin2x) dx + ex + 2xy -y rin 2x) dy=O

A:

Q: Intergrate:

A: To evaluate the integral.

Q: (§5.5, Q34) Calculate the derivative d dæ ), Vi dt.

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Q: 3z cos(z)dz

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Q: Ssin^3 (2/3 x) cos^4 (2/3 x) dx

A:

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your v?

A: Solution

Q: Find dy/dx by implicit differentiation 4 cos (7r) sin (6y ) 5

A: We have been given an implicit function and we are supposed to find dy/dx.

Q: tan(4x + 8). Find the differential dy when x = Let y 1 and dæx 0.3 Find the differential dy when x =…

A: In the given question we have to find dy of the function at both of the given value.

Q: -5 1 -dx Jo 2x+4 1 dt 2 V6-t 1 ii) S,

A:

Q: find the differential dy if y= sqrt(2x^5-3x

A: Given query is to find the differential of the expression.

Q: solve using homogenous and exact. (2x-3y)dx+(2y-3x)dy=0

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Q: Find the derivative dy dx || dy dx of the function y = sec (₁ +√4+ sin ¹(4 + ²))

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Q: solve  sin(x)dy/dx + ycos(x) = cos(x)[ex + sec2(x)].

A: Convert into dy/dx+p(x) y=Q(x)

Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

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Q: х2 9 dy + sinx - у %3D0 dx

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Q: dy Obtain general solution of- 3/xy dx

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Q: 3. (2х - у - 4) dx - (х-3)dy -0 when x %3 1, y 3D 4.

A: We try to identify and group terms and integrate.

Q: sin(3z+z²) Find y' for y = (6 – 2*)3

A:

Q: f(x csc² 2x - x cos 2x)dx

A: The given integral is ∫xcsc22x-xcos2xdx. The objective is to solve the given integral. Following…

Q: Test for homogeneity

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Q: What is the derivative of y = (sin (3x?)2? dy dr 12z sin' (3교2) VI-974 dy dr 12z sin (3z²) VI-9z4 dy…

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Q: tan(2x + 2). Find the differential dy when x = Let y : 4 and dx 0.2 Find the differential dy when x…

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Q: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

A: