(x-2) (x³-4) Vx² +1 dy 1. If y = then equals to : dx

Q: d'y & dx Find d'x to the : dy *yーy=7 %3D7

A: We have the expression x2y2-y=7. Differentiating both sides of this equation with respect to x, we…

Q: Find P.S. of (16x+5y) dx + (3x+y) dy = 0 If the curre to pass thru the point (1,-³)

A: The given equation is: (16x+5y)dx+(3x+y)dy=0⇒(16x+5y)dx=-(3x+y)dy⇒dydx=-16x+5y3x+y⇒dydx=-16+5yx3+yx

Q: a. By differentiating x2 - y2 = 1 implicitly, show that dy/dx = x/y. b. Then show that d2y/dx2 =…

A: The given equation is

Q: dw 2+2 (B) Given w-f(z) 3D to find dx

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Q: If x=t² - 5t and y=1-61² , then dy at t =1 is dx Oa. 4 O b. -1 - 4 d. 4

A: We need to find parametric differentiation

Q: dy Зу +4 Find the general solution: %3D dx 2y + 3

A: Topic - differential Equationd By separating Variables method

Q: dy ху+3x-у-3 7. Ans: y-x+In y+3, %3D = C dx ху-2х+4у-8

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Q: -3 dx dy 0, y2

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Q: If x = 2t2 +t+1 and y=8t3+3t? + 2 then dy at t = 1 is dx

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Q: If x = t - t3 and y = t2 – t4, the value of at t = 2 is dy dx

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Q: Find P.S. of (16x +5y) dx + (3x+y) dy = 0 If the curre to pass thru the point (1,-3)

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: d²y ex 1. Find dx2 for y = %3D (2x²–3)

A: According to our terms and conditions I have solved first question for next question repost

Q: d²y 2) Obtain a particular solution for d*y dx+ + + y = x³ + 2x +1 dx2

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Q: dy Find dx x = 7 y = 2-1

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Q: dy if y = Find dx et %3D 4x2-3x+2

A: Differential of function

Q: dy y dx 2x = 3y2 – 2 when y = 1 and x = 1 in terms of x. %3D - -

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Q: x³ex? (Xie, 2010) y In y dy 2. dx

A: Given query is to find the solution of the differential equation using seperation variable.

Q: I Solve the fllowing FODF 2y(x+y+2) dx + (y²-x²_ 4x-1)dy = o when x=2,y= 3

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Q: C. dy b. 4 sin 2x> , y = 2, when x = 2 %3D dx dy С. dx = x + 3+ e2x>, y = -1, when x =

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Q: = 2-x² and f'(2) dy when x = 1. dx 8. Let y f(1+ Ju), - 3.Find

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Q: •1 fl-x r4-x²-y 16. x dz dy dx 0 Jo 3

A: See the attachment

Q: If yx^2 + y^2 = x, then the dy/dx is

A: Using derivatives formula.

Q: dy -: y = 6x² – 4x, dt dx = 7,x = -2 dt (5) Find -

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Q: dy %3D -9y = 0 with the conditions that x = 0 and dx

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Q: - 2y 4 given that y = 3 and 4 when x = 0. Solve dx2 %3D %3D dx

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Q: dy Find dx2 4 if y = x cos(x) d²y dx? ||

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Q: If x =t-1+5 and y=6+t2 then dy at t dx = 15

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Q: If x=t - 3t and y=1-21² , then dy at t=1 is dx a. – 4 b. -1 4 O C4 d. 1 | 4

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Q: Find the solution y = y(x) of dy y2 +y dx 0, x3/2 subject to y(1) = 1.

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Q: dy/dx 5 - y = In(x – Vx²+ 1)

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Q: df Find and dx of dy 2 2 f(x,y) = /3x +4y?

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Q: Find dy/dx2 implicitly in terms of x and y. x*y – 6x = 9

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Q: 8) a) Find dy/dx if: e3x = x+y b) Differenctiate y = (sin r)"

A: We know that general derivative of d(xn)/dx is nxn-1. And derivative of d(sinx)/dx = cosx  d(lnx)/dx…

Q: If y = = e2a + e3x, then d y at x = 0 equals dx3 %3D

A: Given: y=e2x+e3x

Q: (d) , 2x Vx2 + 2 dx -5 (e) Si J5-y dy

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Q: If x=t² - 5t and y=1-61 , then dy at t=1 is dx

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Q: If x = 1 + t3 and y = 5t – t² then dy at t = 1 is : dx 2 3 None 3

A: Find the derivative of y with respect to x using chain rule

Q: dx dy Explain your solution to the problem: = x + 3y – 2t², 3x +y+t.+ 5 dt ||

A: Given the system of differential equations:              dxdt=x+3y-2t2                  ......…

Q: find d^2y/dx^2 implicitly in terms of y and x  2y^3=3x^4

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Q: Find the solution of: dy 2y 3x when x = 1, y = -1 dx 2у + ||

A: A differential equation of first order is said to be homogeneous if it is of the form dydx=Fyx. It…

Q: (3x -y - 4) dy t (x+y-4) dx = 0, 2. 14

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Q: - +5. dx + 6y = 12(x+e") 1 dy given that y =- and = 3 when x

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Q: If y=u³ and u = 4x² - 2x + 5, give dy dx

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Q: dy , Suppose x and y are variables that satisfy the equation x² – y³ = 12. What is dx %3D - dy 3y2…

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Q: Find the solution y = y(x) of y2 dy + y - dx = 0, x3/2 subject to y(1) = 1.

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Q: Find y subject to the conditions dy/dx = 2x – 3 and y(0) = 3.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.