1. y' = csc x - y cot x

Q: (sec? t + csc² t) dt

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Q: find dy/dx at the given point. (x + 2)2 − 6(2y + 3)2 = 3, (1,−1)

A: Given that  (x + 2)2 − 6(2y + 3)2 = 3 Differentiating with respect to x

Q: Differentiate the function. 7x - 1 y = 3 5x° + 7 y' = D %3D

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Q: 1+vx [8] Find y" of y =

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Q: Jx -Jx-15 = 3 JX-15 =Jx - 3 X-15= Salvethe equation

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Q: Equation is homogeneous ? (y²-2xy) dx=(x²-2xy) dy True / False ?

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Q: (16x + 5y)dx + (3x + y)dy = 0 the curve to pass through the point (1,–3) %3D

A: The solution of the problem is given in the next steps.

Q: Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dy…

A: To find the slope of the tangent line to the curve  at the point .

Q: 2 Solve equation (D² +1)y-secx tan x using method of variation of parameters. %3D

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Q: Let xy = 2y + x. If you implicitly differentiate this dy equation, and then solve for you dx (a-y)…

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Q: Differentiate the function. y = (3x* - x+ 1) (-x³ +9) %3D y' =] %3D

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Q: The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy4 + 2y)dx + (2y³ + 2x²y +…

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Q: d'y + k?y = 0 Give the degree of the equation dx Give the order of the equation (x* + 2y)dx – xdy =…

A: We need to tell the degree and order of the given differential equations:

Q: The point on the curve y=vx+2 which is closest to the point (5,2) is

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Q: (ex + 1)²e-y dx + (e* + 1) 5e-* dy = 0

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Q: Consider the curve given by y² = 2 + xy. dy dx (a) Show that = 2y-x (b) Find all points (x, y) on…

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Q: dy as a function of x. Write the function in the form y = f(u) and u= g(x). Then find y = (- 2x +8)…

A: We know that ,  if y = f ( u ) and u = g ( x )  Then  dy / dx = f ' ( u ) • g ' ( x )

Q: (x2 + y? )dx + 2xydy = 0.

A: We can solve this as follows:

Q: Find dy/dx.  Y3 + (y+2)2 - 1 - x2 = x

A: Expand the left hand side expression and isolate the variables x and y.…

Q: Solve (3x²y³+4xy)dx+(3x³y²+2x²)dy=0

A: Let us considre the differential equation Mdx+Ndy=0 The equation is exact ∂M∂y=∂N∂x The solution of…

Q: Solve (e²y - y) cosx = e sin2x dy dx Select one: O a ev + 2yev-e2cosx = c O b. e+ ye+e-2cosx = c Oce…

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Q: dy + (ax – 7)y = bx° dx %3D - a = 2 andb = 1 dy + (2x - 7)y dx = x² 6.

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Q: 3c The gradient of the curve which passes through the point (2,12) is given by 5x + 7 dy dx Find the…

A: The solution is given as

Q: V1-x² 1–x2 dy dx -1 . J-V1-x²

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Q: linear first order equation y dx = (e + 2xy – 2x) dy %3D

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Q: 7. Find an equation of the line tangent to the curve y = 3x² – 1 and perpendicular to the line x

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Q: dy + (1x dx 7)y = 2x°

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