y sec t+sec t tan t + (2y+tan t) dt dy xy - (x+2y)2 dx 3y(x' -1)+(x' +8y- 3x) dy -0: y(0)=1 dx

Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

Q: of and for the functions: dx dy H.W: Find 1. f(x, y) = (xy-1)² 3. f(x, y) = (x²-1)(y + 2) 2. f(x, y)…

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Q: Find y': y=- Vx* + 4

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Q: 3 tanx dx 3/ secx

A: Indefinite integral: An integral which does not have any upper limit or lower limit of integration…

Q: (1+x*)dy + x(1+ 4y²)dx =0

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Q: xcos² (8)dx + tan(8) dy = 0, y(1) = 8 У (1)

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Q: V= tan -¹ (y/x) verify vxx+vyy=0 or not

A: Given, V=tan-1yx     Verify Vxx+Vyy=0 or not

Q: (16x + 5y)dx + (3x + y)dy = 0 the curve to pass through the point (1,–3) %3D

A: The solution of the problem is given in the next steps.

Q: Air is being pumped into a spherical weather balloon. Atany time t , the volume of the balloon is…

A: a) dV/dr means the rate of change of volume with respect to radius.  dV/dt means the rate of change…

Q: ctan x (2) Let h(x) = t dt, calculate h'(T/3). ww. t2 + 2

A: Solve the following

Q: xy Find all second order derivatives for r(x,y)= 4x +9y

A: The given function is

Q: -x-1 a) y' = +2yi-1 v(0)=1

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Q: Find the equation for the curve f (x) at the point (x, y) meet the following conditions dy / dx = 4x…

A: A curve is a function with equation of the form y=f(x). A differential equation is an equation in…

Q: dx S (x² – 6x + 13)² 4.

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Q: Find the partial derivative dz for the function z = cos(x³ +y²).

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Q: find dy y = sec-1 (e-x)

A: According to the question, we have to find the derivative of the expression y=sec-1e-x. To…

Q: x+y y² +1 #2) (x + tany)dx +- -dy = 0.

A: here we have to solve the differential equation.

Q: ( 3x²y + e' )dx + ( x³ + xe' - 2y)dy=0

A: We will first check whether given equation is exact or not ,then we find general solution…

Q: x° + x2 + 1 (c) dx. x3 – x2 +2x - 2 arctan x (d) x2

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Q: Consider y=(x2+1)2x a) find dy/dx b)Evaluate y'(1)

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Q: Find general solution of ODE   (x+y-1)dx-(x+y)dy=0 dy/dx = (x+2y-3)/(2x+y-3)

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Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

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Q: dy_x² +2x(1+x*) tan" x (1+x*) dx O Op tion 1

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Q: By using chain rule Find dy/dx iff- u=-1, x=-1

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Q: r1/V1-x 70. (2y + 1) dy dx |-1/Vī=x

A: Consider the provided integral ∫-11 ∫-11-x211-x2 2y+1dydx. Solve the provided integral. ∫-11…

Q: Find y' and y". (x – y)3 = x – xy + 1

A: Topic :- Derivative

Q: FTnd the General/Practical solution FoT +he Following DTFFerentiat equation. {x-9x? + 16x - 144)y?dy…

A: The differential equation is given as x3-9x2+16x-144y2dy=2x2-1e4ydx find the general solution.

Q: Solve dy dx Option 1 - y tan x = -y² secx 1- y = sec² x + tan x + C 3- y = secx + tan² x + C 2 y-¹…

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Q: dy of the curve yln x + 5x² + y' = 13 at the point (1,2) dx b) Find

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Q: v (m/sec) 0 A 2 3 4 6 →t (sec) -2/ f(x)dx

A: Solution:Given       for x=5  y=0and x=3     y=2f(x)=5-xTo find∫35f(x)dx=?

Q: If y=x^(2)+81, find the relationship between (dy)/(dt) and (dx)/(dt) Where x,y depend upon t.

A: We have to find the relationship between  and where  and  depend upon .We use Chain Rule to answer…

Q: 2xydx+(x^2)dy=0

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Q: find dy/dx x(х+1)(х- 2) (х*+1)(2х+3) 25) у%3 43) у%3D 1+(lin x)? 1+(ln x)?

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Q: Use implicit differentiation to find dy/dx 4G - y = 2x = 2- 4y dx O dy. 2-dy dx

A: It is implicit derivative.