Find d²y/dx² for the following equations: e) xy +y2 = 1

Q: Obtain the general solution to the equation. y(dx/dy)+6x=3y^4

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Q: d/dx (dy/dx)` x=1, , where y = x3 + 2x - 11

A: To find: The value of ddxdydx at x=1. Given: The function is y=x3+2x-11. Formula used: Power rule of…

Q: Evaluate the integrals

A: ∫01∫0x2∫0x+y2x-y-z dz dy dx

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

A: 2y(x2-y+x)dx+(x2-2y) dy =0M.dx+N dy =0M = 2y(x2-y+x)N = x2-2yNow.            dmdy =…

Q: (x + y – 2) dx + (x – y + 4) dy = 0 |

A: Given:-(x + y - 2) dx + (x - y + 4) dy = 0To find: Find the family of equations

Q: dy dx\, Given that x = t e and y = 1² e“ +1¸ Find = - 1

A: We have to find derivative at that point

Q: dy 2х %3D (Зу + x)— dx

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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: Find dy/dx in terms of t if x = t – t°, y = 2 + 9t

A: Given, Now differentiate with respect to t we get, dxdt=1-3t2dydt=9

Q: dy If x = t - t3 and y = t2 - t, the value of at t = 2 is %3D %3D dx

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Q: Obtain the general solution of the equation d'y +6 dx dy ? + 10y = 50x dx %3D

A: Given : d2ydx2  + 6dydx+10y = 50 x

Q: dy 4. a2+ y? = ry (Bernoulli DE) dx

A: Answer and explanation is given below..

Q: If yo is the particular solution of dy 4x y, y(0) = 3, dx find the value of yo(2).

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Q: If xy + y2 = 1, find the value of d2y/dx2 at the point (0, -1).

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Q: d'y Calculate y = eX + e* dy %3D dx2

A: It is known that if  we have a function f(ax) then the derivative of the function is,   Here it is…

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: NOTE: Enter the exact answer. yz dx dz dy -180 J–120

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Q: Given a+ yx = e¥ , what is 1-y dy dz 1+y dy 1+y dz 1+y el-I

A: Given equation is x+yx=ey We have to differentiate the given equation. To differentiate given…

Q: If y = t“, then dy 4t³. dt

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Q: Obtain the general solution to the equation. dx y dy + 6x=5y

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Q: M(x,y) + N(x,y)*dy/dx = 0 ? is it Exact Equation?

A: Consider the equationMx,y+Nx,y×dydx=0provided that there exists a function ψ(x,y) such that∂ψ∂x=Mx,y…

Q: Show that y=xe-x satisfies the equation dy/dx +y=e-x

A: We find dy/dx using product rule

Q: NOTE: Enter the exact answer. r3-y 5y dx dy

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Q: Rewrite the equation with the variables separated. dy + Vỹ = e# /G dx dy (e – 1) dx dy (e + 1) dx dy…

A: Rewriting the equation with the variables separated.

Q: Find dy/dx fc (1) y = x³ Inx ,,2

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Q: dy dx +y =xy², y(0)3D 1/2

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Q: dy Find a solution of x dx y2 - y that passes through the indicated points. (a) (0, 1) y = | 0

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

A: Using derivatives formula.

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: dy -y- dx 2x, given that when y=0, x=+2

A: We need to solve the given differential equation with its initial conditions. As the equation is of…

Q: Find at the given point without eliminating the parameter. dx2 1?, y = , X = 2 t = 2 3

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Q: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

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: Find a solution of dy (x³ – 1) = y2 – 4 | dx that passes through the indicated points. a) (0,1) b)…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other…

Q: Find dy/dx and d²y/dx2. x = e*, y = te-t

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Q: dy y3Dx dx Inx Find

A: y=xlnxTo find dydx

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

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Q: For which value of a the equation dz dy dx =2 -1 does hold?

A: The constant rule of integration and the power rule of integration are given by and, respectively,…

Q: NOTE: Enter the exact answer. c6 V36–z² xy dy dx dz | 0. 0,

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Q: The value of C in the equation: dV/dt= -500(t+1)^-2, when V=700 and t=0 is?

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Q: Given the IVP dy + 4y = x - 2, y(1) = 0, dx the value of y(2) is closest to

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Q: Find the solution of the equation dy -y = x dx | subject to the condition y(1) = 2. %3D

A: Given differential equation is xdydx-y=x and y(1)=2

Q: Find dy/dx if y = J' V1 + ² dt. Explain the main steps in your calculation.

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Q: dy 2 ,? cosx +-y = -x²y dx %3D

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Q: dy Find the equation of the solution to dx x°y through the point (x, y) = (1, 2).

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Q: = y° dy dx

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