v°dx + x (x + v) dv = 0

Q: If x? + y2 = 100 and dy/dt = 9, find dx/dt when y = 8. (Enter your answers as a comma-separated…

A:

Q: t'dx dt X(1) =2 Salve this (Ivp)? IHomework

A: the given differential equation is t2dxdt=x2 therefore,dxx2=1t2dt integrating both sides…

Q: Given f(x, y) (8a®y + 3xyf). Compute: dx?

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Q: dy at the given points. dx Find 5. x + 4xy + 2 y² + 3 = 0 .2 at (2,–1).

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Q: dy Find the value of at t = 1 if dx? Vt2 + t, y = t2 + 3 x = 4

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Q: 12. Use the substitution x = sec 0, where 0 < 0 < T/2 or T < 0 < 3#/2, to evaluate Vx2 1 dx x*

A: We will evaluate the given integral by using substitution method as shown below

Q: dy Given that y = 5u+ 4 and x = -u', hence find dx

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Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

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

Q: Q2/ Find the extremals for : i) JW) = dx. ii) J(y) = S,v² +y² + 2ye*)dx.

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Q: Use the attached equation to find  dy/dx for this: 5tan−1(x2y) = x + xy2

A: Given, 5tan−1(x2y) = x + xy2

Q: *f(x,y) = xy + aS lšl fry.fyx gl y²+1

A: Given fx,y=xy+eyy2+1

Q: dz Given z = 4x2 + y²,x = sin t, y = t2, find : dt

A: Topic = Derivative

Q: 7 dt, where x> 2 Find dx for y = J 31+7 3

A: We shall use the Newton Leibniz formula

Q: Find dy/dx for the following functions:- (2) y = v sinh Vtan x (4) y=2,u = 3x²-2 u²+1

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Q: Vx +1 dx x + 2 (b)

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Q: For the given DE with coefficients linear in two variables, do the following: (6x – 3y + 2)dx – (2x…

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Q: dy is equal to- dx If y = !, then the value of +3 V1 +y* V1+x

A: Introduction :

Q: FIND dy AND d?y OF x= VI-t AMD y= t° -at dx

A: Given x=1-t , y=t3-3t

Q: Q2/ Find the extremals for : y" dx. JW) = | i) ii) Jy) = S,(v² +y² + 2ye*)dx.

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Q: ôf Find dx fe for the following dy and x?y (a) ƒ(x,y) = y4 + 3

A: Consider the given function: fx,y=x2yy4+3 Here, the objective is to find the value of ∂f∂x and ∂f∂y

Q: dy olve the O.D.E’S y + 4 = 2x using separable of variables. dx

A: Here is the solution:

Q: dz = 2ni to deduce that z+1 Use the fact that (x+1)dx+ydy Sc O (x+1)dy-ydx = 0 and Jc (x+1)²+y² =…

A: Given ∫c1z+1dz=2πi ......(1)we have to prove that ∫c(x+1)dx+ydy(x+1)2+y2=0 and…

Q: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: IV. Find of the following. dx = V1-t 1. ly = V1+t %3D 3t X = . 1+t3 3t? y = 1+t3 tま- 2.

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Q: (ztan 2 +1) dx – x dy = 0

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Q: ) PV Is AN ALTITVOE TO OI メーD エF 41 = Sx+S エ FINO Mメエ

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Q: f(x, y) = 2x- xy + y, find (a.)and (b.) at (Xo, yo) didirectly from the definition. dx dy

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Q: B) Find Sx e2x dx, at h = 0.2, use Simpson's 1/3 rule. J0.4

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Q: dx Find the value of at y=1 if x=z³+4z and z= dy (y? + 2y)²/3.

A: Given,         x=z3+4z  and  z=y2+2y23

Q: | f(x)dx = 25 what is 11' | f(s)ds? Given that

A: We change the variable to x from s

Q: dy Given that y = In 9x, find dz dy

A: Use derivative rules to find dy/dx

Q: dz Q2 Given z = xw? + cos y + wx , w =t, x = 2t2, and y = 3t, find dt

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Q: Find the general solution of this DE using INSPECTION. dnda + +(x? t y?)dx = 0 2 aycdly

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Q: dz Given z = 4x? + y²,x = sin t, y = t², find - dt

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Q: By algebraic substitution, the integral dx dx is converted to: 4+Vx dy y+4 2 dy y+4 ydy y+4 2ydy y+4

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Q: ds where t+s = 2s . dt Find %3D 6.

A: t+s=2s

Q: Find fr and fy- f (x, y) = 8e dt

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Q: Find the value of d-y/dx at the point defined by the given value of t. x- 6t 2 -3, y= t 5, t=1 3D1…

A: Take the derivative than eliminate the extra terms as required.

Q: Q2) Evaluate , S2 xsiny? dy dx 0 Jx2

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Q: dx dx is converted to: 4+Vx By algebraic substitution, the integral - 2ydy y+4 B y+4 © [ vdy y+4 dy…

A: Given, u= ∫dx/(4+√x) We can solve it by substitution method.

Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

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Q: Given y is the square root of x. Find dx/dt when y=2 and dy/dt= 1.75

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Q: The antiderivative of [Vx²-25 dx is x2 – 25 – sec-lx+ C. A True B) False

A: ∫x2-25xdx

Q: dz Given z = e* sin y,x = u² + v²,y = uv, find dv

A: Using chain rule of derivative,

Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…

Q: dy Find dx Let y = Show your work. Væ +1"

A: Consider the given function, y=xx+1 the quotient rule of differentiation is, ddxuv=vdudx-udvdxv2…

Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t

Q: dy Given y = vx² – 5x, evaluate using delta process. - dx

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Q: Find (a) PSD of U(t) = X(t) + Y(t) (b) Sxy (@) and SXu (@) %3D

A: Answer: For the given data, we get

Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.