Given the autonomous first-order differential equation ーア(1-) dx

Q: find the general solution of the first-order linear differential equation. y' + (tan x)y = cos x

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Q: Solve the Linear first Order Differential Equation xdy - sin dx

A: See the attachment

Q: What function satisfies the differential equation y - y' = 0?

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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: ху xy' = y(1+ln2)

A: The given differential equation is  xdydx=y1+lnyx

Q: solve the first order of differential equation dy/dx = y2 -4 using seperable method

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Q: Find the solution of the differential equation y"+y' = sin x %3D

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Q: Solve for the non-homogenous linear differential equation: y''+4y=cos^2(x)

A: Given; y''+4y=cos^2(x)

Q: Find the general solution for the first-order differential equation. dy dx 16x

A: We have to find general solutions of given equation.

Q: find the general solution of the first-order linear differential equation. y' − (ln x)y = xx

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Q: Obtain the general solution of the given differential equation: tanydy = sin3xdx

A: The given differential equations tan2y dy=sin3x dx⇒sec2y-1 dy=143sinx-sin3x dx    As…

Q: Find the general solution of the differential equation for interest compounded continuously,dA/dt =…

A: dA/dt=kA

Q: Solve the given differential equation by separation of variables. dy -4x - y dx

A: We have to form in a integrable form.

Q: Find the general solution of the first order differential equation 2xy(dy/dx)=x2-y2

A: The given differential equation is a homogeneous. See attached file for a step by step explanation.

Q: What is the particular solution to the differential equation with the initial dx condition y(-2) =…

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Q: Solve the 1st order differential equation y3+x-1 y = x dx

A: Given differential equation is y3dydx+x-1y4=x. Note that the differential equation is of the form…

Q: Solve the given differential equation by finding an appropriate integrating factor to make it exact…

A: Given equation is the linear equation  of the form  dxdy+xP(y) = Q(y)  and integrating factor is…

Q: Find the general solution of the first-order linear differential equation y′ − y = 10

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Q: Solve the given differential equation by separation of variables. 8y dx

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Q: Solve the given differential equation by separation of variables. 4y dx

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Q: Find the solution for the second order differential equation y-4y = x sinh x.

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Q: What is the linear differential equation of the bernoulli’s equation dy/dx-y[1/(2x)]-y^5=0?

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Q: у" - 2у' + у %3D et + Зех 1+x2

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Q: dx at + tx + = 0

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

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Q: Find the general solution of the first-order linear differential equation xy′ + y = x2 ln x for x…

A: The first-order linear differential equation ,  xy'+y=x2lnxfor x>0. Solve the equation for the…

Q: The Bernoulli's form of the differential equation xdy - [y + xy³ (1 + ln x)]dx = 0 is

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Q: form the differential equation corresponding to (y – b) = 4(x -a) %3D

A: Given: The equation is (y-b)2=4(x-a)   To determine: The differential equation from the equation…

Q: (D – 3D + 2) y = (1+ e-")?

A: I am attaching image so that you understand each and every step.

Q: Find the general solution of the first-order linear differential equation for x > 0. dy = 30x + 14…

A: Consider the given information:

Q: Find the general solution of the given differential equation

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Q: Find the solution of differential equation 4 dx2 +y = sin).

A: The given differential equation is 4d2ydx2+y=sinx2. Find the solution of the differential equation…

Q: ylv – y" = 4x + 2xe-*

A: the

Q: (メyーx+24 -2) dx- (x+ 4x) 0

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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: dy. = | + X + xy +メ dx

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Q: Solve the given differential equation by separation of variables. dP = p-p² dt

A: The given differential equation is: dPdt=P-P2 We have to solve the given differential equation using…

Q: Find the general/particular solution of the given differential equation:

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: find the general solution of the first-order linear differential equation. xy' + y = x

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Q: Solve the given differential equation by separation of variables. e-y + e-5x - y exy dy dx

A: To find the solution of D.E.

Q: Find the solution of the Linear Homogenous Differential Equation Cofficients. D²(D + 2)*y = 0 =D(

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Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

A: To determine the Bernoulli's form of the differential equation x3y dx+3x4-y3 dx=0.

Q: The solution of the differential equation: y - = y? is

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Q: (D² + 4) y = tan 2x

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Q: dy_ y²sec² (-) tan (-) dx x2

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Q: Consider a differential equation y' = xy + xe -x

A: To solve a differential equation:

Q: Convert y'=Xy ʻ-y into an exact differential equation.

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Q: The solution of the exact differential equation (ycosx + 2xe") + (sinx + x²ev – 1)y' = 0 is:

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Q: Solve the given differential equation by separation of variables. dp = p-p² dt

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.