By using the substitution z = cos y, show that the differential equation dy cot y dx X can be reduce to dz Z dx X =e¹ csc y Hence, solve the original equation when y(1) = 0.

Q: Find all solutions of y" = ln x

A: We have to the differential equation.

Q: dy Solve the differential equation = -3 cos x-4x if y(7)=0. dx

A: To solve the given differential equation.

Q: Solve the differential equation 2 ď²y dy + 4y = cos(ln x)+x sin(ln x), r > 0, dr dr? by using the…

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Q: If y=-2x² + sin x solve for the differential of dy.

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Q: 8. Solve the differential equation (x+y)² dy = a². dx

A: Let x+y=t This implies 1+dydx=dtdx

Q: A system of pulleys will be needed to assemble the cable tower on site. A differential equation…

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Q: M= Cos(xyz)+log3(xyz)-Csc-1(xyz) solve= ∂3M/∂xyz

A: Given;                  ∂3∂xyzcosxyz+log3xyz-cosec-1xyz…

Q: x(2y – 3)dx + (x2 + 1)dy = 0

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Q: a - Find h (Stet sinh t sint dt)

A: The objective is to find ∫te-3tsintsinhtdt It is known that, sint=et-e-t2isinht=eit-e-it2…

Q: 1) Find the second derivative of y = csc 2 e cot 2e %3D

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Q: Solve the differential equation dy + 2y sin x cos x = 4cosx dx cos?x subject to y = 3 when x = .…

A: The given differential equation is cos2xdydx+2ysinxcosx=4cos5x.....(1) with condition y=3 when x=π6

Q: dy +x Sin ( 2y) – xe-x Cos ² y = 0 dx

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Q: Solve the following Clairaut equation   y=xy'+(y')^2

A: Firstly we will differentiate this equation to get simpler differential equation

Q: Find the 3rd derivative of (1 + 2y)³ + eª (sin² y) - 3y cos(e=? )

A: Given data (1+2y)3+ex(sin2y-ycosex2=3y and find 3rd derivative or d3dx3=?

Q: (2) Solve the differential equation dy sin x, y(0) = 3. dx

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Q: find the first & second derivative of fox)=e 2. Cosx.

A: Given: The function fx=x2excosx, To find: First and second derivative of given function fx.