(a) Suppose u(x, y) = y³ – 3.x²y is harmonic, then find its conjugate harmonic v(x, y). %3D

Q: 7. Find dy dx (a) y = (x* + 5x) cos 5x, %3D

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Q: d²y If y=cos 4xr, then at x = 0 dx?

A: Given,     y=cos4x

Q: Find the solution to the Bernoulli Equation. (3siny - 5x)dx + 2x²cotydy=D0 O x³(siny- x)2 = Csin?y O…

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Q: dy 3. dx y – x + cos - -

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Q: You tart muesting at t=0 y co) =0

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Q: Given a6x CosT+Sy - .3x. -Siny+ 10x-e -*, defermine (1) T'=S(T) ax T'-

A: Given:T"=6x2y3-cosx+5y2-siny+10x2-e-3xTo determine:i  T'=∫T"dxii  T'=∫T"dy

Q: -п/2 сп/2 w L cos dz dy de (ху

A:

Q: If Xy +y.1 find the value of dy dx 2 5- at the point Co,-1)

A:

Q: dy at t= T is dx If x=t+sin 2t , y = 3t – cos 2t, then O a. -1 O b. 1 O C. -2 O d. 2

A:

Q: 2) Obtain the DE with respect to x of (x - h)² = 4(y-k).

A: Sol

Q: Q3 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: The given function is, y3secx2+y2=cos2x

Q: 5*-1 a) If y =Vx* +sin (5x)+ 2 then dy fınd dx b) If y = e2*sinx, then show that d²y =…

A:

Q: y=(4x -5x +6)(e-sin 2x), then find dy at x 0.

A:

Q: d’y dy xe" (3sin r -4v = e* cos r Ans V -Ce2X 1e (C cos rd C. sin r) cOS r

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Q: z= cos y Using the substitutions the DE (3cos y - 5x) dx – 2x?tan y dy=0 reduces to dz= - sin y dy

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Q: y= A cos at a solution to y" + 3y = 0 such that y' (1) = 2? %3D

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Q: y = sin x, y = cos.x , x= 0 , x=- is revolved about the x-axis T/2

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Q: 1. Find y' a) y= X fanx In3 b) y= 3 <) y = (cos@)r2 %3D

A: Since you have asked multiple questions, hence we are solving the first question for you. If you…

Q: e2 (2 cos y dx – sin y dy) = 0, y(0) = 0 – sin y dy) = 0, У (0) %3D

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Q: 2 3 Evaluate: y cos(z5) dx dy dz 0

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Q: (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 (y – cos?x)dx + cos x dy = 0 + Ri = E, where L, R, and E…

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Q: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

Q: ZX = 24, XY = 10, and YZ 26. Find cos Y. %3D 5/12

A:

Q: 2. [sin y -ysinx]dx+(cos.x+xcos y+2y)dy=D0 (4x°y-4xy)dx-(x-x dy D0 3.

A: Given that: (y2+4x2y-4xy)dx+(x2-x3)dy=0

Q: Take the derivative of this integral.

A: Given

Q: Q3 Find dy/dx on the graph y3 sec /x2 + y2 = cos2x at point (1, 2).

A: We have to find the derivative  of given expression at point (1, 2)

Q: 17. Determine the value of fx dy - y dx, where x(t) = (cos 31, sin 3r), 0 ≤ ≤n.

A: The given integral is: ∫X x dy - y dx, where Xt=cos 3t, sin 3t, 0≤t≤π The components of the…

Q: 5-2x dy if y = cos Find dx %3D 5+ 2x

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Q: III 6(x3 + xy²) dv, where E is the solid in the first octant that lies beneath the paraboloid z = 4…

A: Given,       ∬∫E6(x3+xy2)dV,       z=4-x2-y2

Q: d*y _2d'y dx d²y_gdy +4y = 0. dx dx dx Ans.: y= (C, +C,x)e* +C, cos 2.x + C, sin2x.

A: Given the homogeneous linear differential equation with constant coefficient is…

Q: If y = (2x² – 3x+4)(e¯* – cos 4.x), then find dy at x = 0 dx

A:

Q: 1. a- Find a result by using variable separation for dy dx b- y³y+x³=0

A: Note:- These are multiple questions and acording to our company guideline we can do maximum 1…

Q: ;+ 2リ+y = ハ- cos(t) Slove the D- E t2 with. Ze Vo initial cuudition s En gineer ing Analysis

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Q: (1 + cos 2y) dr - 2r dy = 0, y(1) = i %3D Oy = Arctan 2 O y = Arctan O y = Arctan ( 1) D y = Arctan…

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Q: 5 Find *: (a) y = cos(11x + 2x) dy

A:

Q: 7. Find fSp(x - y)*dx dy, where D is Figure 17.2.13. y A シ=V ソ=2-

A: Answer is 64/35

Q: 2. If xy+Y find the value of dy dx2 5- at the point Co,-1)

A:

Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

A:

Q: 1. Find fx,fy,andfz f(x,y,z)=sin(xy)cos(yz2)

A: It os partial derivative wrt x y z

Q: 16. 1) Given that y+x-2y 0, find in terms of x and y. dx ii) Given that x =t'. y 1/t, find in terms…

A: Derivative of implicit and parametric function

Q: dw 3) Find ifw = 5 cos(xy) – sin(xy),x = ,y = t,z = t³ - %3D dt

A: Given: w=5cosxy-sinxy, x=1t, y=t, z=t3 For finding dwdt, first we find w in terms of t So, we put…

Q: 3 T - 2 Evaluate: J. Soves y cosx³dy dx

A:

Q: b- y" -y+2y+ cos x, 05x y(0) -0.3, y()--0.1

A: To show the boundary value problem has unique solution we solve the given ode by method of…

Q: me general solution of (D²-2D+1)y=2sin > A y=c1eX +C,xe* + sinx+cos x y=C1eX +C,Xe* + sinx ©…

A:

Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

A: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

Q: S-* cos(x²)dxdy = Q2): Show that 1-y2 %3D 6.

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.