Take y′′ + 5y = 10x + 5. Find (guess!) a solution

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Q: Solve the given DE using 3 possible solutions: y' X 3 - 2y 3 3xy 2

A: Given DE  y'=x3-2y33xy2  …………………………(i) we can write it as dydx=x3-2y33xy2

Q: Solve : t -4t y"+2y - Sydt e s(t-3) yro) = 0 , y'co)= 0 y'co) = 0 %3D

A: Step:-1 L ∫0t fu du =1sFs L ft δt-a  =fa e-a s Ly'' =s2 ys -s y0 -y'0Ly' =s ys -y0 Step:-2 Given…

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A: In the question it is asked to calculate the solution of differential equation 3y'''+2y''+y'-9y…

Q: . Find the general solution of the first-order equation y? – 2ry dy dr

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Q: Find the solution. y'• ty ty" © y- (1-c, y- - (1-co")

A: We have to solve y'+ty=ty3 This can be written as: y'+ty=ty3⇒1y3y'+tyy3=t⇒1y3y'+ty2=t⇒1y3dydt+ty2=t…

Q: find the general solution of the given equation. 3y'' - y' = 0

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Q: Consider the equation (34)x = (3y)s where x and y are unknown. The number of possible solutions is

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Q: Find a general solution of the equation: 5xy' = 2 – y %3D

A: Please find attachment for the details solution

Q: X 3. Solve the equation y'+ xy = with the Bernoulli substitution method. y

A: To solve the following problem, we use the Bernoulli substitution method. Then the problem convert…

Q: solve the DE y'' - 5y' + 6y = 32xe2x, y(0) = 1, y'(0) = 0

A: *Concept:- the give differential equation is Linear differential equation of higher order with…

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

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Q: Find all solutions of the form y = erx for the equation y''−y'−2y = 0. Then write the most general…

A: This is a second order differential equation. The solution of a second order differential equation…

Q: Q1. (4 marks) Find the general solution of the Cauchy-Euler equation: ry - 3ry + y = , 1>0.

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: ?The Third Equation for i3 7in+12i3-=-3-O 5i1+12i3=0- Zir-4i2+16i3=-3- 0

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Q: y'e² 3-2х y' = y– xy

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Q: Q2\ Find the general solution to the given Euler x?y – 3xy' + 9y = 0

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Q: Verify that x and x* are solutions to x²y" – 6xy' + 12y on (0, 0), and give the general solution to…

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Q: Solve for z. If there are no solutions type DNE: 1 -4%3= I- 4 4z - 16

A: x4x-16-4=1x-4

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A: Given y dx-(2xy+y2)dy=0

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A: We have to solve given problem:

Q: Let y(x) be the solution for the DE: y = (x+y+ 2)2 If y(0) = -2, then find y() %3D

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Q: Find the general solution y" – 6y'+9y=x*e*

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Q: (2x2y+3y3)dx - (x3+2xy2)dy = C Solve for Particular Solution when x = 1, y = 1

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Q: z = xy dy x2+y= 2x/1-x’y² dx 2. Using the substitution ,change the to a separable equation. Hence…

A: We are given the differential equation  xdydx+y=2x1-x2y2 we have to use the substitution z=xy.

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Q: Solve the Bernoulli equation. 3xy' + y = y¯8 x>

A: We have to solve

Q: Given y1 = Vi a solution of 4t²y" +y= 0. Find a second independent solution.

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Q: Find the general solution to  y''+ y' = 1 + 2sin(2t)

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Q: Find the solution to y - x+t y' = y if r(0) = 5 and y(0) = 4. %3D

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Q: 2. Solve the diophantine equation x = y'.

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Q: find general solutions (for x>0) of the Euler equation x2y"+7xy'+ 25y = 0

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Q: Find the general solution of the given second-order differenttial equation y" + 18y' + 81y =0 y(x) =…

A: we have to find the general solution of the given differential equation. y"+18y'+81y=0

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Q: — хz + 2ху %3 0. xy ay az az Solve, y? ax

A: Lagrange's Method: Let us consider a standard form of the first order partial differential equation…

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A:

Q: 2. Find the general solution. y' + sec x y = cos x. а. b. y' +y =÷(e* -e-*).

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Q: Find the general solution of y' = y sec x

A: Given, The differential equation y'=ysecx We have to find the general solution.

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Q: Find the particular solution of an EDE (2xy2 +1)dx + (2x2y-y)dy%3D0 when x-2 and y=-2 Answer:

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Q: The Cauchy-Euler equation can be reduced to an equation with constant coefficients by means of the…

A: For the solution follow the next steps.

Q: Ex/solve The equations 2x-y+3Z= -5 using Sing Gram e %3D X+y - Z = - 1 -2x+3-2Z%3= 2 。 メ= -1 -2 -1…

A: 2x-y+3z=-5x+y-z=-1-2x+y-2z=0 by using Cramer's rule- x=D1D, y=D2D, z=D3D D=2-1311-1-21-2…

Q: d²y 4 + y = t2 –- 2t + 3 dy - dt2 dt

A: As per the guidelines, are supposed to solve only one problem, please re-post the other problems…

Q: The general solution of the DE y" -y" + y'-y 0 is

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Q: Obtain the general solution to the equation. * + 2x = 4y° dy The general solution is x(y) = |…

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

Q: Using the substitution x= X -3 and y= Y-3 show that the equation dy y+3 dx x+y+6 can be reduced to a…

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Q: 1: Find the general solution of the following equations: I. dy_2r+2y-3 X-y-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.