Observe that y = x is a particular solution of the equation %3D 2x²y" + xy' – y = 0 and find the general solution. For what values of x is the solution valid?

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. xydx - (x + 2)dy = 0

A: Given problem:- Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS.   xydx -…

Q: Find the solution of the DE using variation of Parameters y''' - 3y'' + 3y = (ex/x)

A: The given problem is to find the solution of differential equation using method of variation of…

Q: Solve for the particular solution of the non-homogeneous DE. y'' + y = 2x

A: Solve for the particular solution of the non-homogeneous DE. y'' + y = 2x

Q: Find the general solution of dy -2x6 dx y-4

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Q: Find the singular solution to the Clairaut equation y = xy' + In(- 19 -y').

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Q: y(4) + 2y" = 2

A: Here we need to find the particular solution of given differential equation. The solution is…

Q: y" + y = 2x

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Q: the solution of the homogenous equation (хусот х -)dy - Ydx = o

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Q: Find a continous solution satisfying the equation and the initial condition (1+x²)y/ +2.ry = P(x) r,…

A: we have given a first order differential equation with piecewise function P(x) we need to find a…

Q: Give a particular solution for y"– 2y' + y = ; ex 1+x2

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Q: fin the general solution of (x+2y-4)dx - (2x+5-y)dy=0

A: Please see the below picture for detailed solution.

Q: I. Find the general solution of the following: 1. dx dy -2x + 3x² dy 2. dx = 3e-2x 3. (x² + 5)dx –…

A: Differential equation problem....

Q: Find the general solution for the homogenous equation of y′′ − y′ − y = 0.

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Q: Give the general solution of xy²dy = (x³ + y³)dx in explicit form.

A: Given differential equation is  which is homogeneous differential equation.

Q: Solve each of the equations. Integrating Factors (3x² + y² + 4) dx + (x² – 2x y) dy = 0

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Q: (r²+y + y³) dx – x dy=0

A: →∫1a2 + x2dx  = 1atan-1xa→ddxuv = udvdx + vdudx

Q: Obtain the general solution valid near the origin: 8x^2y" + 10xy' − (1 + x)y = 0

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Q: Find the general solution of (x^2+x)dy=3dx

A: Given difeerential equation, (x2+x)dy=3dx

Q: Find the general solution of the equation xy' = ky that is valid for x > 0.

A: We have to find y(x) for this equation which is valid for x>0. We use integration to solve this…

Q: A solution of a DE which is not exact and falls under Case 3 i.e. a2 can alone be solved by b2 DE…

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Q: Solve for the particular solution of the non-homogeneous DE. 2y'' +y' = 3

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Q: Find the general solution and particular solution of this equation. (Non-anonymous question) xydx +…

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Q: y" + y" = 3

A: Solving the given third order differential equation

Q: Give a particular solution for y" – 2y' + y = ex 1+x2

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Q: x²dx + y(x-1)dy = 0 %3D

A: We need to find solution of differential equation.

Q: Obtain the general solution to the equation. (x² +19) dy dx + xy - 2x = 0 The general solution is…

A: Using integrating factor method

Q: x²y"+xy'-y= x 2

A: Given Cauchy-Euler equation is x2y''+xy'-y=x.

Q: Find a particular solution to æ' = -x – y + e', y' = 2x + y – ešt using undetermined coefficients.

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Q: 2y" + y' = 3

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Q: The equation y dx + 2x dy = 0 can be converted to Exact using integrating factor Then the solution…

A: Please see the answer in step 2

Q: Solve for the particular solution: dy + 를y3D -2°y"; y(-1) %3D2 dz

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Q: Solve for the general solution * (4xy+3y – x) dx + x (x + 2y) dy = 0 x' (4xy² + 4y – x) = c x²…

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Q: he equation ay"+ by' + cy = 0 has a unique solution satisfying y(0) = 1 and y'(1) = 2.

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Q: y" = 4

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Q: Find the family of solutions of the equation (x2y5 + y3)dx + (x3y4 + x)dy = 0

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Q: Solve for the general solution xydx - (x² +2y² ) dy = 0 x² = 4y° In(2 ) xy = 4y° In() Option 1…

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Q: Find the general solution of the equation: anu dyn = 0.

A: Given equation is ∂nu∂yn=0   To Find: General solution of above equation.

Q: y +y² – 1 = 0, Yı = 1

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Q: Apply the appropriate method to solve the Cauchy-Euler equation 2x²y "+ 5xy'+ y = x² – x

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Q: Find a general solution to the DEQ w" + 4w = sec*(2t)

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Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D. Answer:

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Q: (Think homogeneous) Solve explicitly (y² - xy) dx + x²2dy = 0

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Q: Find the general solution of y" + 2y=ex +2.

A: The Auxiliary equation is D2+2=0 solve for D Therefore  D=±-2=±2i Therefore the solution is…

Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D0.

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Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D0. Answer:

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Q: Solve the bernoulli's equation x(6x^2−y−1)dy +2ydx =0.

A: The given Bernoulli’s equation can be written as:

Q: OBTAIN THE GENERAL SOLUTION (x - 1) dx - (3x - 2y - 5) dy = 0

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Q: Find the general solution of y"+25y=sec(5x)

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