Find the general solution, using separation of variables: dy dx

Q: dy Find for y = dx V7 – x2 dy dx

A: Differentiate  y with respect to x

Q: Find d2y/dx2 implicitly in terms of x and y.

A: we have;  xy-1=2x+y2 ................................(1) differential equation with respect to x

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

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Q: Solve the attached equations  by the method of undeterminedcoefficients.

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Q: dy c) Hence find the solution when x = 0, y = 0 and 1. dx

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Q: dy Find for dx 2. y = x(e*) = x(e*)

A: Given: y=xex   ....(1)   As we know that; The Product rule; f·g'=f'·g+f·g' And ddxlnx=1xddxex=ex

Q: Obtain the general solution to the equation. dy y +7x +1 %3D dx

A: Here we have to find general solution of given differential equation

Q: What is the value of I V16 – x² dx?

A: The definite integral ∫-4416-x2dx can be solved by applying the trigonometric substitution . Let…

Q: Find the solution. dy y -xy? dx

A: This is a problem of differential equation.

Q: Find dy/dx x = 2eθ , y = e−θ/2

A: Given:  x = 2eθ  and y = e−θ/2

Q: Find dy/dx in terms of a and y if x?y – x - 4y – 10 = 0. dy dx

A: To find the derivative w.r.t x using implicit differentiation.

Q: Find dy/dx in terms of x and y if x8 + y? = V10. %3D dy dx ||

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Q: dy Find the general solution of 2x² = a? + y? dx %3D

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Q: dy X+y dx

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

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Q: dy if y = 53*, than dx %3D

A: To find dydx for y=53x Let u=3x then y=5u So, y is a function of u, and u is a function of x. So to…

Q: Given that x2 -y² = 9, then dy/dx = %3D

A: Topic = Derivative

Q: Find dy/dx and d2y/dx2. x = et,    y = te−t

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Q: dy Find for y = dx /9 – x4 dy dæ

A: see below the answer

Q: Find the first and second derivatives. -3 y = 5x - 11x -8x dy dx d°y dx? %3D

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Q: Solve the Linear DE: 2y (y2 - x) dy = dx. %3D

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Q: Find a solution to the SDE dX; = X,(ydX; + tdt), where y ER is a constant and Xo = 1.

A: The given equation is dXt=XtγdXt+tdt. The given initial condition is X0=1. The integration formula…

Q: dy Is y =V10 – X a solution of dx

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Q: Differentiate implicitly to find dy/dx. -y2 = 7 x2 + y2 %D .2 dy dx %3D

A: Given that, xx2+y2-y2=7

Q: Solve the differcential equation dy = xy - x, given that y = 2 when x = 0, expressing y in terms of…

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Q: Solve the equation dy y° – y, - dx? dy giving that dx 0 when y = 1 and y = 2 when x = V2. %3D

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Q: What is the numerical approximation to -dx -1 2+x using the basic trapezoidal rule? (a) 0 (b) 2 (c)…

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Q: For the equation, y(x+y+1)dx + x(x+3y+2)dy = 0, what is dM/dy - dN/dx?

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Q: dy + 4y dx 31 with y W differen ナけ:

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Q: Given z = 1le lle*y® , find 10 dz dz dy

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Q: Solve: (r* + y") dy = xy dx

A: we have to solve the given differential equation . (x2+y2)dy=xydx

Q: V1-x² e-(x²+y²) dy dx

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Q: x dy dz= y dz dx z dx dy.

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Q: By using appropiate substitution, solve dy hpT i. x2 dx 1 = xy – y² ii. – 2. (2х + у)е2»+у | dx

A: Consider the provided question, (b) (i)

Q: Find and in terms of t. dx2 x= -9 sint, y = cost dx dx2

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Q: Solve the general solution dy = 1+x + y? + x²y? %3D dx

A: Given,           dydx=x2 + 1 + y2 + x2y2

Q: dy Find for y = dx V5 x² dy dx

A: To find the derivative.

Q: Find the particular solution of (y + Vx? + y²)dx – xdy; when x = v3, y = 1

A: The differential equation is given as y+x2+y2dx-x dy = 0x dy = y+x2+y2dxdydx= yx+x2+y2x2dydx=…

Q: Solve the equation by using the method of variation of parameters: d2y dy dx = X 2. dx

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Q: Find dy/dx | V(r) =Y/ Tir ³ 3

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Q: Find, the, general solution of 2 dy + y = xe"Inx. dx²

A: Given the differential equation           y''-2y'+y=xexlnx Find the general solution.

Q: d'y dy - -2xe dx dx

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Q: dy Solve dx x+ y and find the particular solution when y(1) = 1

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: dy Given that y = x°e", find dx dy dx

A: In this question, we need to find the derivative of y = x9ex

Q: Use the method of separation of variables to solve, dy 2x(3x +1) Зу? — 1 dx given that y(0) = 2.

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Q: = y° dy dx

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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.