noger whare : y's Fl7. ) Homogencus writter us Example 2: y'- 3yay %3D

Q: ye(2y*) dy

A: Given the integral I=∫ye2y2dy     ....(1)

Q: 2 dydx + f(x, y)dydx

A:

Q: Find dy Y= 5In CI+x") 4 dy'=?

A: The solution are next step..

Q: Qg show that: coths =} hm X+1/, X-1

A: Formula: The relation between hyperbolic function cothx and exponential function is given by, cothx…

Q: cose o3drde =? ans. はは 3一

A:

Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

A:

Q: seclyltun Cy) -csc?(y!dy

A: Use formulas of integration to evaluate the given.

Q: Find S (x + In y) dydx

A:

Q: a) 2 7e"- dy

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

Q: 3 If y= Vx (x-1), find dy (Use rules, not a de finition XP

A: Given:         y=xx-1       dydx=ddxxx-1    Apply product rule:         ux·vx'=u'(x)·v(x)+u(x)·v'(x)…

Q: ) y = 3logst ) y deriv = (sech t) (1 - In(sech t

A: A function's derivative is the function whose value at x is f′. (x). The graph of a function's…

Q: What is fx , where f (x, y, z) = (sin yz)ez3−z−1√y ?

A: Given, f (x, y, z) = (sin yz)ez3−z−1y

Q: Find dydx? for f(x, y) = eXy

A:

Q: What is the difference between dy dy and Ay Use an example y = 4x?+ eX to under stand. 4x2+ ex

A: In the given questioin we have to tell about the difference between dydx,∂y∂x and ∆y∆x. first we…

Q: Ir th line x=4+2t, ーも paralled to the plone 3x +ry +2=7-

A:

Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

A:

Q: (2y) dy. CSC

A: We will start with the substitution, csc-1(2y) = x and apply the integration by parts. And, will use…

Q: Differentiate: y = v25 – 22 – 5 arccos() 5+2 O y = O y = %3D Oy =

A: derivative

Q: tan st dt \+9t?

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

Q: Suppore velue fx) = x". Find Hhe valhe %3D fli.0) using finst-or for appresimaton

A:

Q: in ze2arctao e C Itex) sec (2

A:

Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

A:

Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: Evaluate [y cos (3y) dy

A: We use integration by parts continuously. ∫f(y)g(y)dy =f(y)∫g(y)dy  - ∫df(y)dy(∫g(y)dy )dy Also note…

Q: Use chain rule to find dy/dx for y=u^4/3 , u=x^2+8x+30

A:

Q: dy by implicit differentiatio Find

A: According to the question, we have the the equation,x7y-xy7=8we have to find dydx so,

Q: nS ISIna X -

A: Consider the quadratic equation as x2 – 12x +24 = 0.The formula for the general quadratic equation…

Q: Use implicit clifteren tra fion to find * for the fol llving x*y+ 3xy-x = 3

A: The given equation is x2y+3xy3-x=3 To find: dydx

Q: If u- f(x) where y=J x+y%*34 show thal do

A:

Q: x +y-y° =5

A: The given equation is x2+y-y3=5 We have to find dydx=?

Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: hind dy if y = sin(x")

A:

Q: 3. Stanh3x dx = Jsinh3x, Ssinh3x_ dx %3D u = cosh3x du = %3D

A:

Q: , find dy/dx. х • 7x² V2 + cos³t dt 126. y 125. y = V2 + cos³t dt 128. y 127. y = dt 12 + 1 dt 3 + A

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Sv? – 1),/y dy

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: dy Find if y = In|9 + x|. dx

A:

Q: 2olue dy %3D

A:

Q: Draw a slope field for dy/dx= -6x^2/y.

A: we have to draw a slope field for dydx=-6x2y

Q: If y= V (x-1), find dy (Use rules, not a de finition ) Xp

A:

Q: er dy %3D sec da

A: The given differential equation is exdydx=sec y and the initial condition is y0=1. Solve the given…

Q: differen tiatin, de tomine dx リ= (aH) (xs) 5 (as) (x-+)

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

Q: Evaluate S y³ dy √y² – 1 - by trigonometric substitution.

A:

Q: Find y' and y". y = Vx In y' y" %3D II

A: we have ,  y=xlnx y'=?y''=?

Q: on(1-y)csc²( y) dy

A: This question can be solved using the concept of integration by substitution.

Q: If (Mesin(2x) dx = eSin(2x) + C, then the M is equal to-

A: We will differentiate both sides w.r.t 'x'

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.