2x°dy = y(2x² + y²)dx

Q: dy The equation, ух + In y, dx 3 Vx²-1

A: Given data:     The given differentiable equation is: .   The expression for the linear…

Q: dy y = x-'(a² + x²)¿, solve for dx

A:

Q: Find dx y = 9x -2 dy dx II

A: Given:    y = 9x-2

Q: d²y Find dx2 1 y = ,2

A: Consider the given equation is, y=1x2 Differentiate as, y=x-2dydx=-2x-2-1dydx=-2x-3dydx=-2x-3

Q: dy

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Q: Get the solution: x^2 dy/dx - y^2 = 2xy

A: Get the solution: x^2 dy/dx - y^2 = 2xy

Q: Solve dx/y-x = dy/y+x = zdz/x2-2xy-y2

A: Solve:dxy-x=dyy+x=zdzx2-2xy-y2

Q: V 2 - y2 4(х + y) dx dy

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Q: dy Which is the of the equation y = e 2x+3? dx 2 В. х+ 3 С. 2х + 3 X + 3 2X + 3

A: given  y=e2x+3 find dydx

Q: dy dx 2 x +34-4 4メ+y -3

A:

Q: dy - 2rV1 – y³, -1 < y< 1 dx

A: Given dydx=2x1-y2

Q: dx -x = 2y², dy y(1) = 5

A:

Q: d²y Find xp y = d²y 口 %3D dx 2.

A: topic - double derivative of a function

Q: Find the value of dy/dx when x= 10.74 and y=2.74 for the given equation. y4-y2-2x3-9x =8

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Q: dy cscx(y+2csc3x+2csc2xcotx) - ytanx=0 dx Solve the LDE:

A: First of all we reduce it in the standard form of linear differential equation then find integrating…

Q: xdy = (y - Vx² + y²) dx

A:

Q: Find dx² given d²y given X² – y³ = 5.

A: Given that: x2-y3=5

Q: Find y dx' 1. y (32x)³(x² - 2)

A: Here is the solution

Q: y=(sinx)x    d2y/dx2 ?

A: Apply exponent rule and solve:

Q: d-y dx2 Calculate y = e¯X + e* 1?

A: Given, y= ex+e-x Differentiating both sides with respect to x we have, dy/dx = d(ex+e-x)/dx dy/dx =…

Q: dy 2x2y+y 二 dx

A:

Q: Q7 Find dy using substitution: dx y = csc-(x3 + 1)

A: Put u=x3+1. Then, du=3x2dx Therefore, the expression y=cosec-1(x3+1) becomes,…

Q: (x² + y²)dy dx 7.

A: Given  ∫-22∫04-x2(x2+y2) dydx

Q: dy dx 8x³e-2y y(1) = 0

A:

Q: (x² + y2) dx dy ow urves y = x² and

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Q: colve dx+. y 2х y²-3x² -dy=0 y?

A: Given 2xy3dx+y2-3x2y2dy=0Need to solve

Q: Q4. The degree of the equation is dy d²y dx dx?

A: degree it is the degree of higher order derivative term here higher order derivative is d2y/dx2…

Q: x² – 4y² dy 29, dx - 2хy ||

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Q: find in terms of x and y. dx 18) x =-4y+2y

A: x2 = -4y +2y3 To find dy/dx in terms of x and y

Q: Find y dx2 in terms of x and y. y7 = x° dy dx?

A: Remark: we know that  d/dx (xn ) = n xn-1 , where n is any integer except -1.

Q: find d2x/dx2 ? y=sinh(2lnx)

A: To determine the second order derivative of the function.

Q: Find d^2 y/dx^2 in terms of x and y. y8 = x9   d^2 y/dx^2

A: Given expression is, y8=x9

Q: dy dx x3 2+y²

A:

Q: Y(Gyt-x-4)dx + 2x dy =0

A: let

Q: V -dx x² + 2

A: Given, I=∫xx2+24dx

Q: dy p2 - 9p + 18 = 0 (p = 2) %3D dx

A: The solution is given as

Q: Find dy/dx x = t2 , y = 7 − 6t

A: Given that: The parametric equations, x = t2  y = 7 - 6t

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

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Q: dy Q5/ a) Find 2 if y = esin (2x) dx

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Q: dy = y – xy³e-2x (final answer should be in terms of y) dx

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Q: a) dx² d²y + 9y = -2e3x „y(0) = 1 ,y' = 1 dx

A: From the given differential equation: d2ydx2-6dydx+9y=-2e3x So, we can also write as; D2-6D+9y=-2e3x…

Q: (dy/dx)-5y= (-5/2)xy3 y(1)=1 solve

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Q: y = e² -Vx sec 6x 3

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Q: dx +(1-2x ]& =0 +y-(x+y)*

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Q: Solve the IVP d'y = 4sec 2x tan 2x, y' (0) = 4, y(0) =-1 dx2

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Q: dy х+ 3 dx (x2 + 6х - 3)2 y =

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Q: Find ay/dx. 8x²y - y

A: