3. Show COMPLETELY that the equation 00 y = c >(-1)"x" n=1 is the general solution to the differential equation (1+x)y' + y = 0

Q: 2. Show that y = e-6t satisfies the differential equation y" – y – 42y = 0.

A: We have to verify that y''-y'-42y=0 when y=e-6t. We know that d2ydt2=y''dydt=y'de-atdt=-ae-at So…

Q: -(* +2) Solve for y = y (a) in the differential equation dy if y (0) = 1. No need to isolate y. %3D…

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Q: It is known that h1(t)=e3t2, h2(t)=30e3t2 are solutions of the differential equation 4h" - 12h' + bh…

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Q: 1. Find the general solution of each of the differential equation y" – 2y' +y = 0.

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Solve for the general solution of the below differential equation. y" + 3y' + 2y = cos x

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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: show that y2 = Cx + (1/8) C3   is a solution to the differential equation y= 2xy' + y2 (y')3

A: y2=Cx+C38and given ODE is:y=2xy'+y2(y')3

Q: 2. In the differential equation 4(3x+ y-2)dx-(3x+ y)dy =0, we let

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Q: 5. Find the solution of the differential equation y =- xy + xy³ (Bernoulli)

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Q: 4. Eliminate the arbitrary constant 'a' in the differential equation: y – 2ay' + x2 = a? %3D

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Q: ...... 19. Find the general solution of the differential equation 2x2 =x² + y² dx

A: We have to solve given problem:

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

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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: 1. Solve the differential equation: xy' – y = 2x In x

A: Use linear differential equation concept

Q: 1 3. y' -- %3D xy+x²y3

A: See the details solution in below

Q: 3. If the general solution to a second-order differential equation is given by cie + ce-5, find the…

A: In the question it is asked to solve the differential equations with initial values given.

Q: 4. Find the general solution to the differential equation y²y" = y/ (where y' = )

A: To find solution of the differential equation: y2y''=y'

Q: 6. Find the general solution to the differential equation y" + 2y' + y = x-4e-" Simplify your answer…

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Q: 18.Find the general solution of the differential equation %3D xp xy-y2

A: To solve the given differential equation, first we convert it into separable form, and then we find…

Q: (9) Show that the solution of the differential equation y + y = -6ye» with y(0) = -1 is (e* –…

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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: 5. Find the general solution to the differential equation et y" – 2y' + y 1+ x2 (where y' = )

A: Let us consider the differential equation y''+py'+q=g(x) To solve the equation  Determine the…

Q: 7. In the differential equation 4(3x+ y-2)dx-(3x+y)dy=0, we let the substitution dw =- (Note: We use…

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Q: 3. Show COMPLETELY that the equation y = C (-1)"x" n=1 is the general solution to the differential…

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Q: Consider the initial-value problem (x² − 1)y"+y' + y = ex y(1) = 1 y' (1) = -1 Does the Existence…

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Q: What is the solution of the first order differential equation y(k + 1) = y(k) + 5.

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Q: 5. Find the general solution of the differential equation y=(2y4+2x)y'.

A: Given differentiatial equation: y = (2y^4+2x)y'  Here y'= dy/dx

Q: 6. Find the particular solution to the differential equation: (y +2)y"=3x*y+4y, given: y(0) = 1…

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

A: The given differentail equation is  y(4) + y′″ + y″ = 0.

Q: 1. Choose a solution to the differential equation y" - y = x²e² + 5.

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Q: 2. y-폼-y 1 ミ、 6x 3x2 ||

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Q: 2. A population is modeled by the differential equation: *= 3N (1-) (1-) dt 50, where N(t) is the…

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Q: 16. What is the particular solution of the linear differential equation y' +y = sec e", whose…

A: The solution is given as

Q: y' + (1+ 2x2) .e²²+y = 0

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Q: 1. Obtain the differential equation associated with y=Ax2+Bx+C

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Q: 1. y'- = xy2

A: Solution is given below:

Q: 5. Find a general solution of the differential equation: y" + 4y' = 2x – 1

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Q: 1. Find a general solution for the Differential Equations dy x- -y = x dx

A: As per company guidelines, we need to answer only one question. So, kindly repost the other…

Q: 2- Find the solution of these differential equations : 1. (x – y) = x + y dy dr

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Q: show that there exists a unique solution to the differential equation y'=ln(xy); y(2)=1

A: Unique solution to differential equation

Q: 1. The order of the differential equation 5x- d'y aty + 3x + w'y = 0 is

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Q: 3. Given that y = 1 when x=-1, find particular solution to differential equation dx dy – 3x²y² =…

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Q: 5. (a) Find the particular solution of the differential equation x³ = 1-e²t if x(0) = 2.

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Q: 7. In the differential equation 4(3x+ y-2)dx-(3x+ y)dy=0, we let the substitution dw =- (Note: We…

A: Given differential equation is 4(3x + y - 2)dx - (3x + y)dy = 0

Q: Show that y = ce* + (x + 2)e²x is a general solution for the differential equation y' - y = (x +…

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Q: 5. Find the general solution of the given differential equation y" + 3y" + 3y + y = 0

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Q: 4ху Find the solution to the differential equation dx which passes through the point (0, e). (In…

A: We first separate the variables:dydx=4xylny10lny10dyy=4xdxThen we integrate both…

Q: The particular solution of the following nonhomogeneous differential equation y" – 2y' +y = x² + e¬*…

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Q: 19. (D³ – D)y = x.

A: