Find the particular solution of the first-order linear differential equation    2xy′ − y = x3 − x    for x > 0 that satisfies the initial condition    y(4) = 2.

Q: Find the solution of the differential equation that satisfies the given initial condition. xy' + y =…

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Q: Find the solution of the differential equation that satisfies the given initial condition. xy' + y =…

A: The given differential equation is  xy' + y = y2, y(1) = - 10

Q: Find the particular solution of the differential equation y√(1 − x2) y′ − x√(1 − y2) = 0 that…

A: Given,y(1−x2)y′−x(1−y2)=0This can be written as →y(1−x2)dydx=x(1−y2)ydy1−y2=xdx1−x2

Q: Find the solution of the Linear Homogenous Differential Equation with Constant Coefficients. (D3 +…

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Q: In the given equation , find the particular solution of the first-order linear differential equation…

A: We have  given first order linear differential equation y'+2x-1y=0 Let P=2x-1 and Q=0 Then,…

Q: Find the general solution of the first-order differential equation                       y′ = 2x√(1…

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Q: Find the general solution of the reducible second-order differential equation: x²y" + 3xy' = 2

A: To find the general solution of the second order differential equation

Q: Find the general solution of the given higher-order differential equation. y(4) - 2y" + y = 0 y(x) =

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Q: Consider the nonhomogeneous differential equation: y" - 2y + y = ... (E). Given that y-e' and 2-re…

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Q: Find the solution of the Linear Homogenous Differential Equation with Constant Coefficients. (D² +…

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Q: Find the general solution of the first-order linear differential equation. xy' + y = x³3 + 1

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Q: Find the particular solution of the differential equation 2xy′ − ln x2 = 0, x > 0 that satisfies…

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Q: Find the general solution of the first-order linear differential equation (x − 2)y′ + y = 1, x >…

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Q: Find the general solution of the first-order linear differential equation y′ + 3y = e3x for x >…

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Q: Find the General solution of the homogenous differential equation: y"-6y'+9y=0

A: We need to find the General solution of the homogenous differential equation y''-6y'+9y=0.

Q: Find the general solution of the given higher-order differential equation. y"" + 2y" - 16y' - 32y =…

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Q: Find the general solution of the first-order linear differential equation. 8y xy = x-2

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Q: Find the general solution of the given higher-order differential equation. y (4) - 2y" + y = 0 y(x)…

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Q: Find the particular solution of the first-order linear differential equation     y′ + (1/x)y = 0for…

A: y/+1xy=0 On simplification, we get ⇒dydx=-yx⇒dyy=-dxx Now integrating on both sides, we get…

Q: Find the general solution of the given second-order differential equation. y" - y' - 30y = 0 y(x) =

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Q: Find the particular solution of the non-linear ordinary differential equation. y' = -3y + y², y(1) =…

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Q: Find the particular solution of the first-order linear differential equation (3y + 5) cos x dx = dy…

A: Consider the given differential equation 3y+5 cosx dx=dy,    yπ=0

Q: Find the solution of the differential equation x In x = y(1+ /3 + y2 )y' that satisfies the initial…

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Q: Find the general solution of the given second-order differential equation. 3y" + 2y' + y = 0 y(x) =

A: We need to find general solution.

Q: Find the general solution of the reducible second-order differential equation x?y" + 3xy' = 2

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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 solution to the differential equation dx = -2y, with the initial condition y(0) = 2, is

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Q: Find the general solution of the given higher-order differential equation. y"" - 3y" - 4y = 0 y(x) =

A: Given :y'''-3y''-4y'=0

Q: Find the particular solution of the differential equation y(1 + x2)y′ − x(1 + y2) = 0 that satisfies…

A: y1+x2y'-x1+y2=0⇒y1+x2y'=x1+y2⇒y1+y2y'=x1+x2⇒y1+y2·dydx=x1+x2⇒y1+y2dy=x1+x2dx

Q: Find the particular solution of the given higher-order differential equation. y''' + 2y'' - 5y' - 6…

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Q: Use the initial condition to find the particular solution of the differential equation. y'-e = 0 ,…

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Q: find the general solution of the first-order linear differential equation. 3xy' − y = x−1

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Q: Find the particular solution of the differential equation   y3(x4 + 1)y′ − x3( y4 + 1) = 0   that…

A: the given differential equation is: y3x4+1y'-x3y4+1=0 we have to find the particular solution of the…

Q: Find the solution to the differential equation y' 2ay that satisfies the initial condition y (0) =2.

A: This is Separable differential equation

Q: Find the general solution of the given second-order differential equation. y" - y' - 12y = 0 y(x) =

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Q: Find the general solution of the non-homogeneous differential equation Y” –  2Y’  + Y  =  x2 – 1

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Q: Find the general solution of the given second-order differential equation. y" - y' - 20y = 0

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

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Q: Find the general solution of the first-order linear differential equation y′ + 3x2y = 6x2 for x >…

A: Given: The first-order linear differential equation: y'+3x2y=6x2 for x>0.

Q: find the general solution of the given second-order differential equation.   13-             3y" +…

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Q: Find the general solution of the given higher-order differential equation. + 3y" + 3y' + y = 0

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Q: Determine the solution x(t) of the ordinary differential equations with initial values a. x"(t) -…

A: The Laplace transform, named after its inventor Pierre-Simon Laplace, is an integral transform that…

Q: Determine the general solution of the differential equation: y" – 10ky/ + 25k²y = e², with K a real…

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Q: Find the general solution of the given second-order differential equation. y" - y' 20y = 0 y(x) =

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Q: b) Write down a linear, homogenenous 2nd order differential equation with constant coefficients that…

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Q: Find the general solution of the given higher-order differential equation. у" + 3y" + 3y' + y = 0…

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Q: 9. Find the solution of the separable differential equation that satisfies the given initial…

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Q: Find the general solution of the given second-order differential equation. 5y" + y = 0

A: To solve the given differential equation.

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.