Solve the differential equation (x²+1)y' + 3x(y-1)=0 and y(0)=2

Q: show that function  y1=x-1 is a special solution of the differential equation y'=1 - ( y-x+1)2 and…

A: Given the differential equation y’ = 1 – ( y – x + 1)2 and we have to show that y  = x -1 is a…

Q: (D² - 3D + 2)y = 2e-* +8

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Q: Solution of differential equation xy' - y = 0 (y' = dy/dx) is...

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Q: Solve the differential equation f -e = 2ey by separation of variables.

A: In this question, concept of separation of variables is used. Seperation of Variables The approach…

Q: differential

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Q: Solve the differential equation. xy' + y = 20Vx

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Q: Find an energy function for the differential equation y"=-y3

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Q: By using substitution of x-e' and t = ln(x), find the general solution of the differential equation.

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Q: solve the for the general solution of the differential equation( linear homologous equation): (D2 +…

A: We have to solve the differential equation: D2+2D-1y=0 The given equation is in symbolic form where,…

Q: Solve for differential equation (3x2-2y2)y1=2xy

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Q: A chemical reaction is governed by the differential equation

A: Given, the differential equation                           dxdt=K(3-x)2 where x is the concentration…

Q: Solve the Differential Equation using VARIATION OF PARAMETERS: y''+y'-3y=4sin2x

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: 5. Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y )²

A: We have to evaluate: (y(x) + 1) ( d^2 y(x))/( dx^2) = (( dy(x))/( dx))^2:Treating y as the…

Q: Solve the 2nd order differential equation: y-xy-(y)=1

A: Given the differential equation is  y'-xy''-y''3=1

Q: Find the differential equation by eliminating arbitrary constant  y=Ae-3x+Be2x

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Q: Explain how to solve a separable differential equation of the form g(y) y'(t) = h(t).

A: A separable differential equation is one in which the terms of two variables in the term can be…

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: One solution of the differential equation y''+y'=0 is y=e^-x. A second linearly independent solution…

A: We will find out the required solution.

Q: (D² - 1)y= 2 1+ex

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Q: solve the for the general solution of the differential equation( linear homologous equation): y''-…

A: answer  Y = 9x22+ 3x detailed solution is given below

Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) -…

A: The given differential equation is, y''+2y'-8y=5e-2x-e-x. Obtain the homogeneous solution.…

Q: Find general solutions of the differential equation    (x^2-1)y'+(x-1)y=1

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Q: Use separation of variables to find the general solution of the differential equation. (6 + x)y' =…

A: Please refer the attached image for complete solution.

Q: 2ydx = (x2 – 1)(dx – dy)

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Q: *- 2- 2 - - 2 = 0 dx dx

A: The solution is given below-

Q: Solve the differential equation for the motion of the spring 384x''+1152x'+864x=0   if x(0)=-2 and…

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Q: (9x^2 + y - 1) - (4y - x)y′ = 0

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Q: Solve the differential equation: xy'-2x2y= y ln y

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Q: 3. Form a differential equation by eliminating the constants a and b: y = ax² + bx

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Q: Use separation of variables to find the general solution of the differential equation. (9 + x)y' =…

A: We have,

Q: Solve the non-homogeneous differential equation of 6y"-y'-y=1-x-x?

A: Given differential equation is  6y"-y'-y=1-x-x2

Q: Match the differential equation with its solution. y' - 4x'y = x3 %3D

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Q: This is a differential equations problem.

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Q: Solve the Differential Equation using VARIATION OF PARAMETERS: y''-2y'+1=(x+1)e2x

A: The given differential equation is: y''-2y'+y=(x+1)e2x

Q: (D² − 4)y = 8e²x – 12 -

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Q: Find the general solution of the differential equation using any method         y′ = ln(x2 + x)

A: we have to find the solution of the given differential equation  y′ = ln(x2 + x)

Q: Find the particular solution of the differential equation satisfying the initial condition…

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Q: The differential equation: y²x + y² = x²yy' is solved by

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Q: y' = ycotx + y²cscx

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Q: Solve (first order linear differential equation): y'-3x2y=ex^3

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Q: Solve the differential equation by undetemined coefficients y" – y' = -3

A: Solution- Given y''-y'=-3 ⇒dy2dx2-dydx=-3-----(1) dydx=m ⇒m2-m=0⇒m(m-1)=0m=0, m-1=0≠m=1 Distinct…

Q: Solve the Homogenous Differential Equation: (x² + y³) = xy ху.

A: This question is based on solution of Homogeneous differential equation.

Q: Find general solutions of the differential equation  (x^2-y^2)y'=2xy

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Q: solve the differential equation using the substitution method. (3siny-5x)dx+2x2cotydy=0

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Q: of the differential equation у" - Зу' + 2у %3е-2t

A: Introduction: A differential equation is a mathematical equation that contains one or more…

Q: solve the differential equation xy' - y = 2x ln x

A: Given: xy'-y=2xlnx For finding solution of given differential equation, we convert it in first order…