Solve the following separable differential equations: a. xy'+ 3y = 0, if y(1) = -3 b. yy +x = 1, if y(1) = 1

Q: Find a suitable form for particular solution of the differential equation y5) + 25y3) = 5 – tešt +…

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Q: State the case and solve for the general solution of the given special second-ordered differential…

A: We have the differential equation given by yy''+y'2=y'. We now have yy''+y'2=y'⇒yy''+y'y'=y' By…

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 second-order differential equation. 6y" + y = 0

A: To find the general solution of  6y''+y=0

Q: Find the solution of the differential equation subject to the specified initial condi- tion: y" =…

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Q: Obtain the differential equations satisfied by the given puiiicular solution 4. y = e3x- 5e - 1 5. y…

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Q: 1 3. y' -- %3D xy+x²y3

A: See the details solution in below

Q: Find the general solution of the given second-order differential equation. 6y"+y' = 0

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Q: Find the general solution of the first order differential equation 2xy(dy/dx)=x2-y2

A: The given differential equation is a homogeneous. See attached file for a step by step explanation.

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

A: Given: y'' + 0y' - 16y = -768t3

Q: x²y" - xy'+ 5y = 0

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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: 2. y-폼-y 1 ミ、 6x 3x2 ||

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Q: Find the solution to the Cauchy-Euler differential equation xy' +3y'+y=0.

A: The Cauchy-Euler differential equation of second order can be written in the form:…

Q: Solve the given differential equation with initial condition.  y' = 2y, y(0) = 2

A: given,             y'=2y       and y(0) = 2

Q: Formulate a differential equation that is satisfied by 1. y=Ae2+ Bxe²r

A: To find: The differential equation: Given: The equation is y=Ae2x+Bxe2x. Concept used: Product rule:…

Q: Find the general solution of the given differential equation 1 2 -y' + y = -x(secx)²y2 x2

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Q: Determine the solutions of the following differential equations using Type IV:

A: Given that: (x2-x-2y+1)dx-xdy=0 and y(1)=12

Q: 1. y'- = xy2

A: Solution is given below:

Q: Find the two power solutions of a given differential equation about the ordinary point x=0. 1.…

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Q: Use the method of Undetermined Coefficients to find a PARTICULAR SOLUTION to the differential…

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Q: This is a differential equations problem.

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Q: 1.) Find the general solution to the first order differential equation given below. -3x 3xe 2x y' 4y

A: In the given question we have to solve the given ordinary differential equation of first order and…

Q: 7e-3x+2x² -xcosx y' -6y3

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Q: Determine whether the given differential equations are homogenous and, if so, solve them. 2x + y…

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

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Q: Write down a linear homogenous differential equation (with the smallest order and constant…

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Q: y"+4y=x² sin 2 u

A: See the attachment

Q: Consider the following system of differential equation, with time domain tE (0, I) =--e. (0)-0, (0)…

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Q: Solve the given differential equation by variation of parameters. x²y" + xy' - y = In(x) y(x) = ,X >…

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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: 2y' +y

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Q: Solve for the particular solution yp of the given differential equation: y" + 3y' + 4y = 4x2 — 2х -

A: Given differential equation, y''+3y'+4y=4x2-2x⇒(D2+3D+4)y=4x2-2x          D≡ddx.............(i)

Q: Find the solution of the following Differential Equations by homogenous equation 7) y'=(y-x)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5. Solve the second order differential equation, dx2 + 4+ 4y = cos2x, given y = 4 and dy :3 when x =…

A: 1f(D2) cos ax = 1f(-a2) cosax 1D X =∫X dx

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

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

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Q: yV + 16y = 0

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Q: A/ By using Exact equation solve the first order differential equation 2y² + ye* + (4xy + x² + 2y)y…

A: Topic:- application of differential equations

Q: 4- Solve the following differential equation: (1 + x²)dy + (y − tan−¹(x)) dx = 0 -

A: Given: The differential equation is 1+x2dy+y-tan-1xdx=0 To find the general solution of the given…

Q: dy dx 11 - 4xy, when x = 0, y = 2

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Q: Find the special solution of ele differential equation. = 20x - 4x3 dy dx y with the initial value…

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

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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: - y" – 4y' + 13y = e2*cos3x

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