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

Q: y"-9y=x/e^3x

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Q: ;y(0) = 1 form of yp to solve

A: As per the bartleby guidelines for more than one part only one has to be solved .Please upload the…

Q: General solution of 2xydx+y^2dy=0

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Q: ² - x ²² = y² dz ४x d²z Find the solution of xy' буду

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Q: Solve using implicit differentation.    x ey = 3x-3y

A: Given;   x ey = 3x-3y

Q: Find the solution of the homogenous equation: 2(2x2+y2)dx-xydy=0

A: The given differential equation is  2(2x2+y2)dx -xy dy=0

Q: Find the general solution of dy -2x6 dx y-4

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Q: a) Solve (t3 + y³)dt – ty²dy = 0

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Q: Obtain the general solution y

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Q: Q5. Transfer the Cauchy-Euler equation to a constant coefficient equation and find the general…

A: Given x2d2ydx2+3xdydx-2y=x2sinlnx

Q: Solve for the solution of the DE: y' – 5y = 0

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Q: Solve for x :C+Vz + m = A

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Q: the solution of the homogenous equation (хусот х -)dy - Ydx = o

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

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Q: y'" — 7y' — бу = 0

A: Solution :- This higher order differential equation can be solved simply by using complementary…

Q: Solve 1 . Find a particular solution to a' = x – y + e', y = -4x + y +t using undetermined…

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Q: a) Find the general solution of the equation dªy dy dx² 4- x2 + 3e* - dr4 by using the method of…

A: As you have posted multiple parts,but they are independent so according to our guidelines we will…

Q: Find the solution of the difference equation 2 (2x^2 + y^2)dx - xydy = 0.

A: Given differential equation 2 (2x^2 + y^2)dx - xydy = 0. Now we will find the solution of…

Q: Use the Adam-Bashforth method of the second order to solve the second equation y’=y(x+y) when h=0.1…

A: Given differential equation is y'=y(x+y), step size h=0.1 with initial condition y(0)=1 Let x0=0,…

Q: (3e3ty− 2t)dt + 33tdy = 0

A: The differential equation is given as (3e3ty-2t)dt+e3tdy = 0 Compare it with Mdt+Ndy = 0 then M =…

Q: Solve the first order equation (3r²y + 2ry)dz + (z³ + x² + 2y)dy = 0.

A: In the given question, the concept of the differential equation is applied. Differential Equation A…

Q: Obtain the general solution. 1. y' = xy?

A: We will find out the required general solution.

Q: G) (2x-yJdx + (4x. +y-3)dy=

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Q: Q1: Solve the second order linear homogenous equation: y" – 2ky' + 4y = 0 k > 2 -

A: According to our guideline we can only answer first question and rest can be reposted.

Q: 3y = 3xy' + y'3

A: Solution: Here 3y=3xy'+y'3 Divide both sides by 3 y=xy'+13y'3   ......(1) Let dydx=P Then from…

Q: Solve the equation xydx - (x + 2)dy = 0

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Q: Solve the equation: ydx + 3x – xy + 2)dy = 0

A: Given: ydx+3x-xy+2dy=0

Q: 2xydx + (y^2 - 3x^2)dy = 0

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Q: |2/2r| 2, dx -1

A: Let I is the value of given Integral.

Q: Solve y"-4y'+13y= yo)=-I ,y'co)=2

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Q: A. y– 2y +1 = (x + 1)e²x

A: To solve the given differential equation using method of variation of parameters.

Q: -Find the solution of y"+y' + by = 0 by transforming y = x"u|

A: Put y=xαu in the given equation y'=xαu' y"=xαu" Then the equation becomes xαu''+axxαu'+bxαu=0 Now…

Q: Solve : -4t y +2y -J ydt = e s(t-3) yco) = 0 ,y'co)= o y'co) =

A: Convert the given equation in Laplace domain: s2Y+2sY-Ys=e-34+ss3+2s2-1Y=se-34+sY=se-34+ss3+2s2-1

Q: Solve for x -1 logs : %3D 3 243 O V5 No Solution

A: Use logarithmic identity:-  (i)  logaa = 1 (ii) bloga = logab

Q: Solve f, e-+ n² dt. 6.

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Q: ) Find the general solution of the DE y = (2+y')x+ (y')².

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Q: Find two linearly independent solutions of the equation (x-1)y"+y=O for |x|<1

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Q: dv Solve ax + by + c dx

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Q: Give the general solution of: dw/dx + (4w)/x = x3

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Q: Solve using the method of variation of parameters y" + 3y' + 2y =: 1+ e*

A: Given that: y''+3y'+2y=11+ex

Q: x In x dx Show that , V4 – x² dx = (2n + 3v3).

A: Part (a) Given integral is ∫12xlnxdx

Q: Solve (mz-ny)p+(nx-lz)q=ly-mx

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Q: Solve the following equation. | (2t – 6) dt = 0

A: Recall the rule of integration: Integral of xndx = xn+1

Q: Find the general solution of y" + 2y=ex +2.

A: The Auxiliary equation is D2+2=0 solve for D Therefore  D=±-2=±2i Therefore the solution is…

Q: 2. Solve the IVP: *+ 2y = te-2", y(1) = 0 dt

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Q: Solve for the general solution. d³x dx -7. - + 6x = 0 dt3 dt

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Q: Find the general solution of y"+25y=sec(5x)

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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.