Solve the difference equation yn+1Yn + Yn+1 + 7yn + 16 = 0, with the initial condition y1 :-7.

Q: y4) – 2y"+ y = 4cos (x+ 3)

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Q: Find the general solution of the equation x2y" + 2xy' - 2y = 0

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Q: Solve the equation dy =- 3y + 5x, yci)=4 2

A: The general solution of the differential equation is, y = x³ + c/x² , where c is the constant of…

Q: Find the solution of the this differantial equation. x2y' = y2 + xy +x2

A: Given: x2y'=y2+xy+x2 For finding solution of given differential equation, first we divide given…

Q: 4. Obtain the general solution. y"-4y'+4 y=3e²*

A: for the solution we have equation y" - 4y' + 4y = 3e2x so now characteristic equation of this is...…

Q: find the general solution of the given equation. y'' - y' - 12y = 0

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Q: Find the general solution of the given equation y''  - 4y = 0

A: The differential equation y''+4y=0 is a second order differential equation. So we find its…

Q: Solve the second-order equation xy" + 2y' 8x? by making the substitution u -y'.

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Q: у" — у' — х %3 0

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Q: Find the general solution to: y(x² +1) + y' = 0, for y > 0.

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Q: Solve y" + ω2y = 0 by method (c) above and compare with the solution as a linear equation with…

A: Consider the given differential equation y"+ω2y=0

Q: Find the solution of y"-y'-6y = -e* +12x with y(0)=1, y'(0)=-2 by method of undetermined…

A: The Auxiliary equation is D2-D-6=0 Solve for D  D2-3D+2D-6=0DD-3+2D-3=0D-3D+2=0D=3,-2 Therefore, the…

Q: Use undetermined coefficients to find the particular solution to y''−4y=2e^−3t

A: Use undetermined coefficients to find the particular solution toy''−4y=2e^−3t

Q: Solve the following equations  by the method of undeterminedcoefficients. y" - 3y' - 10y = -3

A: The given differential equation is y''-3y'-10y=-3. The auxiliary equation of homogenous part of the…

Q: 5. Find a particular solution to the equation -2x y" + 4y' + 4y = xe¯

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Q: Find the general solution y''-y'-2y=0

A: Given the differential equation y''-y'-2y=0. We need to find the general solution of the above…

Q: Find the general solution of x?y – 2xy + x²y² + 2 = 0 by first determining a particular solution in…

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Q: - Solve the equation z = x² + xy² when x = = 0, zz = y³ and when x = 2, z = y.

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Q: dP/dt = P - P2 ; solve by seperation of variables.

A: It is required to solve the given differential equation using separation of variables. dPdt=P−P2

Q: find the general solution of the equation. y - 4y = 2e" V.

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Q: Solve the initial value problem (t2 – 5)x' – 2tx = -2t(t² – 5), x(2) = 7.

A: Given differential equation is t2−5x'−2tx=−2tt2−5......1 and x2=7. We have to find the solution of…

Q: 3. Solve the DE: Y'=e2x+ 3y.

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Q: Solve the following equations  by the method of undeterminedcoefficients. y" - 3y' - 10y = 2x - 3

A: The solution equation is obtained by the equation y=yc+yp Take the characteristic equation of the…

Q: The particular solution (yp) of the equation y" - 3y' + 2y = 5 e* is yp = -5xe* False True

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Q: Find the general solution of EonC(2)'y/n-1),

A: ∑i=0nnCi(2)iy(n-i)

Q: Solve the following difference equation with initial conditions: 12Yn + Yn+1 = Yn+2, Y₁ = −2, Y₂ =…

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Q: у" - у' + 4y %3D 0; у(-2) %3D 1, у'(-2) %3 3

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Q: Find the general solution of the given equation. y" - 3y'-4y = 0

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Q: Find the solution of y − y = e2x , y(0) = 1.

A: Substitute value of the variable given in the equation. Then after calculation the value of other…

Q: Find the particular solution of r*y – y y+1 ; y (3) = -1

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Q: Find the general solution of æ²p+ y²q = (x + y)z.

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Q: Find the solution to the Bernoulli Equation. 2x³y = y(y²+3x²)

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Q: Q4- Solve y"- 4y' + 13y 3x.e*

A: Topic:- differential equations

Q: a. Solve x2 + 2x-y+1%30 and x + y-1=0 using Elimination Method

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Q: Find the general solution of the given equation 2y''  - y' - 3y = 0

A: Given:              2y''-y'-3y=0   Solution:               We can solve this equation using :…

Q: Find general solution of the difference equation Yn+2 + 6yn+1+9yn = n 2" +7, by method of…

A: Given:  The given difference equation yn+2+6yn+1+9yn=n2n+7

Q: Find the general solution of the equation y" – 2y + 2y = 0

A: We have to find the general solution of the given differential equation y"-2y'+2y=0

Q: The solution of y – 6y – 2y = 0 is -

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Q: 2. Find the stability of the difference equation xn = Xn-1+¤n-2.

A: By theorem,            Let the 2nd order homogeneous differential equation is,…

Q: Solve the general solution y" - 8y'+ 16y = 0 1.

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Q: Find the solution of y' = (1 – 4x) y², y (0) = –1 in explicit form

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Q: Solve the equations by Gaussian elimination: 4x + 6y – 2z = 8 6x + 9y – 3z = 12 -2x - 3y + z = -4

A: Solution using Gaussian elimination is given below

Q: Solve the IVP: y" + y' = 0 y(n) = 0, y'(1) = 2, y'"(n) = -1

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Q: Solve the difference equation A?yn + 3Ayn – 4y, = n² with the initial conditions yo = 0, yn = 2. %3D

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Q: Solve the general solution y" – 5y' + 6y = xe*

A: Given problem is : y'' -5y' +6y = xex We have To find:- General solution of given differential…

Q: Solve the 2-step difference equation 2n1-1 = 2, n1 = 1. %3D 3 3

A: to solve the given equation

Q: Use the method of undetermined coefficients to find the particular solution y, y" – 4y" + 4y' = 2x –…

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Q: Solve for the particular solution, yp- y" - 6y' + 9y = 6x +2– 12e* y(1) = 0; y'(1) = -1

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.