Find the general solution of dy + y cot(x) = 6 csc'(x). dx

Q: x COSI dz dx dy

A: Simplify the integral

Q: State the order of homogeneity and solve the differential equation as a homogeneous equation. x dy…

A: See the attachment

Q: sinx dy = 0 y cos xdx + 1+

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Q: Find the integrating factor of the non-exact differential equation: dy= (e2x+y-1) dx

A: Given differential equation is dy=e2x+y-1dx which can also be written as e2x+y-1dx-dy=0 Comparing…

Q: Solve the first order differential equation dy ycos' x 1+ sin x dx

A: The given equation is first order, linear differential equation.

Q: Find the solution to the differential equation dy x In x cot y = 0. dx

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Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: To determine the general solution of the differential equation.

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Given differential equation

Q: Use integration to find a general solution of the differential equation       dy/dx = e2−x

A: dydx= e2-xdydx= e2e-xdy = e2e-xdxThis is variable separable form

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: The given differential equation is dydx=x3y. Solve as follows. dydx=x3yydy=x3dx

Q: Use the integrating factor technique to solve the following differential equation and its initial…

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Q: Solve the differential equation: dx/dy*(sin(x)) + y*(cos(x)) = sin2(x)

A: It is differential equation.

Q: Find the general solution to the differential equation using undetermined coefficients. y" + 5y =…

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Q: What is the linear differential equation of dy/dx+2xy+xy^4=0 using dv/dx?

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Q: Find the solution of the differential equation tan x dx +tan y dy=0.

A: Here we have to find the solution of the differential equation  tanx dx + tany dy = 0.

Q: Find the general solution of the first-order linear differential equation (y − 1) sin x dx − dy = 0…

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Q: Use a technique of integration or a substitution to find an explicit solution of the given…

A: Cross multiply first to take x terms on a side and y terms on another side. Then integrate both…

Q: Solve the given problem on Integrating Factor for Non-Exact Differential (1 + y?)dx + (xy) dy = 0…

A: Given non-exact differential equation1+y2dx+xydy=0HereM=1+y2N=xyanddMdy=2ydNdx=y

Q: Solve using the non-exact linear differential equation  [ytan(x)(cos(2x))-1]dx+csc(2x)dy=0 when…

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Q: Show that the solution of the differential equation dy/dx=sin(x+y)+cos(x+y) is  1+tan(x+y)/ 2 =…

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Q: Solve the differential equation using simple substitution. dy/dx = e^(x+siny)

A: Given differential equation is: dydx=e(x+siny) Rewriting given differential equation:…

Q: Use a technique of integration or a substitution to find an explicit solution of the given…

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Q: dy -2 sin x where y (5 = JT dx

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Q: dy Vx ev+Vx¸ x > 0 %3D X dx

A: To Find the seperable differential equation

Q: xcosydy + sin2ydy – dx = 0

A: First arrange it in the bernouilli equation then find its integrating factor. Then  use the formula…

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: The given differential equation: dx=x9y dy

Q: Find the general solution to the differential equation dy = tan y. dx

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Q: Solve the given differential equation by separation of variables. csc(y) dx + sec²(x) dy = 0 s(x):…

A: To solve the given differential equation using separation of variables

Q: Explain why the initial Value problem dy/dx=x-cos(y); y(1)=pi has a unique solution. For that…

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Q: Obtain the differential equation whose general solution is y= a sin 2x b cos 2x, where a and b are…

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Q: Show that y is a solution of differential equation = 1-. dy %3D dx

A: y'(x)=1-yx We can simplify it as: dydx+yx=1First-order linear ordinary differential equation.…

Q: Solve the separable differential equation. dy (1+y²) coshx dx 9+sinh x

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Q: Use integration to find a general solution of the differential equation                  dy /dx = x…

A: Given: dydx=x1+x2 Multiply both sides by dx dy=x1+x2dx

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Consider the given D.E. Rearrange the D.E.

Q: Solve the differential equation using separation of variables: dy + y* + y = 0 dx

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Q: ly- cos? x) dx+ cos xdy = 0

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Q: Find the general solution to the given differential equation. (Use C for the constant of…

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Q: Solve the first order differential equation. dy - y ln(y ecos x) dx = y sin xdx

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Q: What is the general solution to the differential equation sin y (x + sin y)dx + 2x² cos y dy = 0 ?

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Q: Given a non-exact differential equation(x - sin?y)dy + sin y dx = 0. Find two integrating factors.

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Q: The general solution of the linear differential equation dx/dy -(cot x) y=sin(2x) *

A: The differential should be dy/dx instead of dx/dy.

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Given a differential equation, dx=x6y dy

Q: Find the homogeneous differential equation achieved by the function Y = 2 e*sin (3x)

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Q: (x²e + y? + xy sin 4) dx – (xy + ² sin 4) dy = 0 -

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Q: Solve the differential equation dy – y² sin(2x)sin²(x) = 0, y(0) = 1 %3D %3D - dx

A: Given that: dydx-y2sin(2x)sin2(x)=0, y(0)=1

Q: Solve the differential equation using separation of variables: dy +y° +y=0 dx

A: The detailed solution is given below Thank you

Q: Determine the order of this differential equation: (dy/dx)6 + y + d5 y/dx5 = cos x

A: We need to deetermine the order of the differential equation given by (dy/dx)6 + y + d5 y/dx5 = cos…

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Given,         dydx=x5y