Find the solution of the following differential equations: (Separable Equations). (1– y²) y' = X 2 ху + 5у + 2х + 10 2х + 3 10y – x + 5, dy 2ху -dx + = 0 у — 6

Q: Find the general solution of the given higher-order differential equation. y"" + 4y" - 9y' - 36y = 0

A: Follow the procedure given below.

Q: The solution of a certain differential equation is of the form y(t)=a^(3t)+b^(5t), where a and b are…

A: Given solution of a certain differential equation is,

Q: 4. find the given general differential solution, using homogeneous equations with constant…

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Q: use the method of variation of parameters to find a particular solution of the given differential…

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Q: Find the solution of the differential equation which satisfies the indicated conditions: 1. y" – 3y'…

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Q: The solution of the differential equation y" + 3y+2.25y = -10e¬1.5x when solved using method of…

A: To uss variation of parameters to find the solution of the given differential equation

Q: 4. Find the general solution of the given differential equations. (a) y" – y" – y + y = 0; %3D - (b)…

A: Given: The differential equation are: (a) y'''-y''-y'+y=0 (b) y'''-3y''+3y'-y=0 We have to find the…

Q: Obtain the solution of the following differential equations. 3. (16x + 5y)dx + (3x + y)dy = 0 ; the…

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Q: solution of the differential equation (x +3) y’ / (2x -3y -4) = 5

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Q: 1. y''''=2y''=2

A: This is a problem of non homogeneous differential equation.

Q: d and classify all the equilibrium solutions of the given differential equation y = (y² – 16)(y –…

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Q: The solution of the differential equation y + 2y +y=2e X using the method of variation of parameters…

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Q: Solve the given third-order differential equation by variation of parameters. y''' − 3y'' − y' + 3y…

A: Given differential Y” – 3Y” – Y’ + 3Y = e5x Hence the homogeneous part i.e. Y” – 3Y” – Y’ + 3Y = 0…

Q: Find general solutions of the differential equation      2x^2y-x^3y'=y^3

A: 2x2y-x3y'=y3 We need to find the general solutions of the differential equation.

Q: Find three linearly independent solutions of the given third-order differential equation and write a…

A: Given equation is: y'''+3y''-6y'+2y=0 Then the auxiliary equation is: m3+3m2-6m+2=0

Q: 6) Solve the differential equation zy" +2(1 – 2) y +(x – 2) y = 2e", if y, = e" is known as a…

A: The given differential equation is:…

Q: Determine the solution of the differential equation 2y"-3y' + 4y = 0 3x V23 y = e (C, cos x+ C2sinx)…

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Q: Find the general solution to the non-homogeneous differential equation using the Method of…

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Q: Find three linearly independent solutions of the given third-order differential equation and write a…

A: We are entitled to solve only one question at a time. So, I am providing you solution of first…

Q: find the solutions of the differential equations that satisfies the given initial conditions:…

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Q: 10. (x² – 1)y" + 2y' – (x – 1)(x + 1)² = 0 %3| - -

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Q: Find the solution of the given differential equation using the method of undetermined coefficients.…

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Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''+4y'+3y=12

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Q: Find the particular solution of the given differential equations. (x² + 2xy - 4y²)dx - (x² - 8xy -…

A: Given equation is (x2+2xy-4y2)dx-(x2-8xy-4y2)dy=0

Q: find the given differential solution, using homogeneous equations with constant coefficients.…

A: Solution: The objective is to find the general solution of the given homogeneous differential…

Q: Find a particular solution of the given differential equation by using the method of variation of…

A: Given, y''-5y'+6y=2ex   ....(i) Auxiliary equation of the given homogeneous equation is…

Q: Find the general solution of the given differential equation using Method of Undetermined…

A: Given that  y4-4y'''+4y''=3e3x+2sinx-8excos2x We have to find the general solution using the method…

Q: Find general solutions of the differential equation      3y^2y'+y^3=e^(-x)

A: Consider the provided differential equation,

Q: Find the solution of the given differential equation. (2r²t-2z') dt + (4z³ – 6z²t + 2zt²) dz = 0

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Q: 9t y - 9 y = e3t

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Q: Determine the particular solution given the differential equations and conditions. 2= 3e* , y = 6…

A: dydx=3ex, find the particular solution and the function

Q: Solve the Higher Order Linear Differential Equation: 1. yIV+16y=0 2. yV+18y'''+81y'=0

A: Topic= Differential equation

Q: Find the particular solution of the given differential equations. 2. (x² + 2xy - 4y²)dx - (x² - 8xy…

A: (x² + 2xy - 4y²)dx - (x² - 8xy - 4y²)dy = 0

Q: Use the method of variation of parameters to find & particular solution of y" – 2y + y = and write…

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Q: is a solution of the differential equation y" + (3x + 1)y' + 3y = 0 , then its coefficients Cn are…

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Q: find the general solution of the given differential equation. 2.y″ − y′ − 2y = −2t + 4t2

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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 particular solutions to the given differential equations: y(3)+3y"-4y'-12y=0, y(0)=1,…

A: The initial value problem is,

Q: 1. Use the undetermined coefficients method to find the general solution of the given differential…

A: Since this image is asked for multiple answers, as per our answering guidelines we are supposed to…

Q: Solve the second order differential equation ÿ + ỷ – 6y = 8e* + 3x 1 A:y = ce2x + c2e-3x + 2e* + 12…

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Q: find the general solution of the given second-order differential equation.   1 -         4y" + y'…

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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: 2. Find the solution of the differential equation ₂ dy 2x² = dx 3xy + y². which satisfy an initial…

A: Solved below.

Q: find general and particular solution of differential equation 4y" - 4y' - 3y = 0 with the given that…

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Q: Determine the solutions of the 1st-order linear differential equations below 3x2y′ = 2y(y −3)

A: Use separable variable method

Q: Solve the given third-order differential equation by variation of parameters. y"' – 3y" + 2y' =…

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Q: (1+ x)y" + (4x + 5)y' + (4x + 6)y = e-2x

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Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''-4y'-12y=3e5t

A: Solve for the particular solution of the non-homogeneous differential equation. 1. y''-4y'-12y=3e5t

Q: –7 + 12 d5x 7) 25 d*x -7- dt5 d²x + 12 dt3 + 8. = 0 dt4 dt2

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