3. Write the general solution of the differential equation whose auxiliary equation has the following roots : m = ±V3,±4,± 2i,-1+ 3i (multiplicity 2).

Q: Obtain the differential equations satisfied by the given particular solution 2. y = 7- 2x +e*

A: The objective of the question is determine the differential equation.   Note -  As per our…

Q: Show that the following differential equation is perfect or not, then find its general solution:…

A: Introduction: Any equation with one or more terms is a differential equation. It includes taking the…

Q: Show that the given equation is a solution to the differential equation written oppos 1) y = e*( x +…

A: given differential equationy'-y=exthen we have to show that y=ex(x+C)be the solution of given…

Q: Find the general explicit solution to the differential equation xyy′ = x2 + 1

A: The given differential equation is xyy'=x2+1 We have to find the general explicit solution of the…

Q: 1) Solve the Bernoulli differential equation with the given initial condition. -2xy = 3y". ) =.

A: okok

Q: Find the general solution to the following Cauchy-Euler differential equation 2 x²y" + xy + 4y = 2x…

A: To Solve: The differential equation x2y''+xy'+4y=2xlnx.

Q: 4. 2a y' = y (y² + 3x²)

A: Given:- 2x3 y' =y(y3+3x2) To find:-.  General solution of given differential equation

Q: Solve the following differential equation using Method of Variation in Parameters y" - 2y' + y =…

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

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Q: Find the general solution of the following differential equation. -2,,4 (2) x²y" – 2xy' = x=2y4 -

A: Differential equation is the combination of variables and their derivative forming an equation. We…

Q: 2) Find the general solution of the following differential equation

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Q: b. 6y²dx – x(2x³ + y)dy = 0 -

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Q: 4. Identify whether y' - 3y = 6 is a linear differential equation or a Bernoulli equation, and solve…

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Q: Solve for the general solution of the given first-ordered Linear Differential Equation y' = x – 4xy

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Q: In the given question , determine whether the function is a solution of the differential equation…

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Q: 5. Find the solution, using variation of parameters, to the differential equation (D³ + D)y = sec²x.…

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Q: Find a particular solution to the differential equation y" + Oz/ – 16y = -768t°.

A: Given: y'' + 0y' - 16y = -768t3

Q: 1) Find the differential equation that would yield the solution given below. y = C1 + C2X

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Q: What is the solution of the following differential equation that satisfies y (1) = 7 and y '(2) = 3?…

A:

Q: In the given question , determine whether the function is a solution of the differential equation…

A: To Determine: y = 3 cos 2x  is a solution of the differential equation y(4) -16 y= 0.

Q: 5. y'+y = xy³; y(0) = 4

A:

Q: 1. Solve (explicitly) the separable Differential Equation du = + with y(0) = 2. y?+1 y(x+1)

A: Given differential equation is first order variables separable differential equation. we have also…

Q: 13.Find a differential equation whose general solution is y = c1e2t + c2e−3t.

A: The given solution is y= c1e2t+c2e−3t.

Q: 2 -1 et x + x' %3D 3 -2

A: The given differential equation can be written as:x'=2−13−2x+ett    and…

Q: 1. Find the differential equation whose solutions correspond to the following equation  y = C1e−x +…

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Q: 1. Find the general solution to the differential equation: y" = 4y' = 12y = tet

A: Given differential equation

Q: In the given question , determine whether the function is a solution of the differential equation…

A: The given differential equation is y(4)-16y=0y=3 sin 2x

Q: 7. x = A + By + Cy² + De-4y; xV + 4x"' = 0

A:

Q: (2xy + x² + x*)dx – (1+ x²)dy = 0

A:

Q: If we use the method of undetermined coefficients, the particular solution of the following…

A: we have to solve differential equation

Q: 6. Use the method of variation of parameters to find a general solution to the differential equation…

A: First we find the complementary function yc and particular solution yp The general solution is then…

Q: Find the general solution for the following differential equation: −(10x+y)+(−(x+18y))y′=0 If the…

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Q: Find the general solution to the following Cauchy-Euler differential equation. X2 y” + xy’ + 4y =…

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Q: 1.3x – xy = c -

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Q: 2 Find the general solution to the differential equation: y"+25y = 20 sin 5x

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Q: 3. (10 — бу + е 3а) da — 2dy = 0 -

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Q: y = cje* + cze²r y" -y – 2y = 0 O 2y " -y' – y = 0

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Q: Find the general solution of the following differential equation: (x^2 + 1)у' + 6ху -х

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Q: Given the differential equation y" – 2xy' + 5y = 0. Determine the first three nonzero terms in each…

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Q: 5. Solve the following differential equation using the Method of Variation of Parameters -2x y" + 3y…

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Q: Solve the given 2. (4) - 2y + y = et +1 differential equation by undermiNed coeFFicients.

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Q: 7. Find the general solution of the following differential equation: V1 + x²dy – xydx = 0.

A: Explanation of the answer is as follows

Q: Find the general solution of the given second-order differential equation. у" + бу' + 9у %3D0 y(x) =

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Q: 6. xy' +y-x+ xycotx = 0

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Q: If we use the method of undetermined coefficients, the particular solution of the following…

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Q: 10- y" – y'= 4x' + 6x

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Q: Find the first five non-zero terms of the solution of the differential equation 2" + xz" + z = x² +…

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Q: 19. (D³ – D)y = x.

A: