find the general equation of : x^3dy+xydx=x^2dy+2ydx  ;y=e when x=2

Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: y =x3 dy Itx² -

A: Note  You type wrong Question here in place of dx/dy must be dy/dx  I solve it using dy/dx otherwise…

Q: Find the first four derivatives of y = 4sinx. %3D

A:

Q: usk 2: Find the derivative of 4x2 + 6y3 = 50 by filling the blanks. %3D (2 xD(x-)+x 6)(y³4)_=__ dy >…

A: We have, 4x2+6y3=50            ⋯⋯1 We know that, from basic derivative formula ddxkxn=n·kxn-1ddxk=0…

Q: Find the partial derivative. 17zy

A: Given, ∂xe17xy∂x We have to find the partial derivative.

Q: as y y = f(x) (10, 4) Tangent line (4, 2) ive your answer to three decimal places.)

A: G

Q: Differentiate: y = 5 tan? (25z) %3D Oy = -750z tan (25z) sec (25r') Oy = -750z? tan (25z) sec (25z)…

A: We have to differentiate  y = 5 tan225x3.

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

A: To solve the given differenrial equation.

Q: Find the equation of the line passing through the point (4,5) and perpendicular to the line y= x+2…

A:

Q: Integrate SxIn x)dy

A:

Q: Find the parabola with equation y = ax2 + bx whose tangent line at (1, –1) has equation y = 3x – 4.…

A:

Q: What is the integrating factor y x² = 2 (2x - y)?

A: The given equation is; y'=2(2x-y).

Q: x3sec2y dy/dx+3x2tan y=cos

A:

Q: Differentiate: F(y) (y + 9y°) yA - y?

A:

Q: If ø = 4xy, find x and y components of the velocity at (1, 4) and (4, 4). Calculate the discharge…

A:

Q: = vt – 2, d²y t – 2. d²y y = t² – 3' dx2

A: x=t-2y=t2-3

Q: 3x V1-x x = 0. y(x) = at Equation of the tangent line

A: Given,           yx=3x1-x2 at x=0

Q: Find the directional derivatives of Ø = x2yz + 4xz2 at ( 1, -2, -1) in direction 2ax – ay – 2az.

A: Answer is in step 2.

Q: Find the parabola with equation  y = ax2 + bx  whose tangent line at  (1, −1)  has equation  y =…

A:

Q: Use differentiation rules to find y' = dy/dx.

A: Rearrange y to get y in fractional form.

Q: find dy/dx

A: y=∫sec x21t2+1dt.

Q: Question 3

A: Consider implicit equation and

Q: If =4xy, find x and y components of the velocity at (1,4)  and (4,4). Calculate the discharge…

A: Given that, ϕx,y=4xy    ...1. Let the points be, x1,y1=1,4 and x2,y2=4,4. Consider the velocity…

Q: find the soution of' the differential eq. System X= 3X+44 9=X+3y %3D

A: Given differential equations are                                     dxdt=3x+4y,dydt=x+3y…

Q: Find the Indicated Derivative dy 1. y = x5 - 3x* + 2x3 - 2x2 + 7x - 1, dx dy 2. y =x2+x-3 + 3, dx…

A: Given:- y = x5 -3x4 +2x3 -2x2 +7x-1 y =0.5x-2 + (2x-3/3) +3 To find:- dy/dx

Q: Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other…

A:

Q: Find dy/dx at the point (2,-2) if 3y2-4x2+4=0.

A: Find dy/dx at the point (2,-2) if 3y2-4x2+4=0.

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: Find anti derivative 3x^2(y^2+1)

A:

Q: Find both first partial derivatives. az

A:

Q: 2T sin (2) dydx 0,

A: To evaluate the double integral, ∫π2π∫0x3sinyxdydx.…

Q: Please show me the partial derivatives for this homogenous equation and solve for GS/PS using Test…

A: Exact differential equation

Q: Find a result by using homogenous for (x³ - 3x²y)dx-(x3³ - y³)dy = 0

A: This question is based on solution of Homogeneous differential equation.

Q: Find dy/dx by implicit differentiation. 5x3 + x2y − xy3 = 2

A:

Q: Find y" by implicit differentiation. 4x3 + 3y3 = 4 %3D

A: Given: 4x3+3y3 = 4 To find: The value of y'' by Implicit differentiation.

Q: Soru 1. (1+ 25)dx + 20* (1 - )dy = 0 ; -) dy = 0 ; + 2ey) dx y(0) = 1,

A: Given that:                           1+2exydx+2exy1-xydy=0    .........................(1)…

Q: 2. [ y dy dx carctan3/2 3 secx 3/2

A: Topic  = Integration

Q: ential equation is given by

A:

Q: Find the derivative of 3 x +7 y = 8 dy %3D dx

A:

Q: ength of the curve 1 1 < x < 2. 6 10x3 +

A:

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: Find dy/dx by implicit differentiation. бх3 + x2у - хуз %3D9 y' = %3D

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: ry' = 3y + y? ху

A: Solution of a nonlinear differential equation

Q: Differentiate the function. 1 y3= (2x +3) dy dx

A:

Q: y 1-

A: The solution is given below in the next step:

Q: Compute the derivative y = dy %3D dt 2t - 7 y = 7t- 3

A:

Q: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Q: Find the derivative of y. y = 3ztanh (z)+3In /1-z y' = 3 sinhz y' = tanh 3z y' = 3 tanhz y' = 3…

A: