Find the particular solution to the given differential equation that satisfies the given conditions. d2y , dy -4x. dy - 2 + y = xe 4X - e = 0 and y = 0 when x = 0 %3! dx2 dx dx

Q: Solve the given differential equation d'y dy +2x- -12y= x' (In x) .2 dx dx

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Q: Soru 1: d²y ²+1 dy +6+9y = e* dx xe(0,+0)a -3x dx?

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Q: Given a differential equation as d²y x2 dx² +4y=0. dx By using substitution of x = e' and t = ln…

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Q: Find the general solution for the differential equation. dy -20xy-5x 0 dx y = D

A: We have to find the general solution for the given differential equation.

Q: Solve the given differential equation: (4x + y - 1)dx + (x - y - 4)dy = 0

A: given differential equation: (4x + y - 1)dx + (x - y - 4)dy = 0

Q: Find the general solution of the given differential equation. y''− 2y' − 3y = e^2t

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Q: Given: dx - (y- 2x)dy = 0, find the solution to the differential equation. O a. 4x - 2y = Ce -2y O…

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Q: Solve the general solution of the given differential equation by making it exact. 1.)(3xy +y' )+(x°…

A: Put y=vx and solve. ∫1ax+bdx= 1aln(ax+b)+C Note: According to Bartleby Guidelines , we can solve…

Q: Determine the value of k that will make the equation exact and solve the resulting differential…

A: Solution :-

Q: Solve the general solution of the given differential equation. Final answer can be expressed…

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Q: Given the function y₁ = x² is a solution to the differential equation x²y" - 3xy' + 4y = 0, find a…

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Q: Find the general solution of the given differential equation. d'y 4 dx dy dy 5- = 0 - dx dx

A: Given differential equation is d3ydx3−4d2ydx2−5dydx=0 We have to find the general solution of the…

Q: Solve the given differential equation by separation of variables: dy 5y dx Oy = cz %3D Oy = Oy = *…

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Q: Find the solution of the differential equation. xdy+(2xy+y-x(e^-2))dx=0 ; y(1)=e^-2

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Q: Determine if the differential equation (3x2y + ey)dx +(x3 + xey - 2y)dy = 0 is or is not exact; if…

A: Given problem:- Determine if the differential equation (3x2 y + ey )dx +(x3 + xey - 2y)dy = 0 is or…

Q: Identify the case of the given differential equation and determine its solution (3x + 2y + 7)dx + (…

A: Differential equation is exact. First show that given differential equation is exact and then find…

Q: Solve the given differential equation: (x - 3) dx + 2 (x + y + 2) dy = 0

A: As per our guidelines I am solving only first question please resubmit other question.  The given…

Q: Solve the given differential equation by using separable variables. 1. dy x-5 = dx y²

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Q: Find the general solution of the given ordinary differential equation: d'y dx² + 4y = 3 e5*

A: The given differential equation is d2ydx2+4y=3e5x. Consider the homogeneous part d2ydx2+4y=0. The…

Q: Solve the given differential equation by separation of variables. xy + 5x - y -5 xy - 2x + 6y - 12…

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Q: 5. dx- 2xy dy = 6x³ y² e¬2y* dy

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Q: Find the solution of the given differential equation. x²y-y ; y (3) = -1 %3D y+1

A: Given,dydx=x2y-yy+1,dydx=y(x2-1)y+1y+1ydy=(x2-1)dxTaking integration on both…

Q: Find the solution of the differential equation 3e?x dy dx -49- which satisfies the initial condition…

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Q: Solve the given differential equation by separation of variables. dy xy + 5x - y - 5 dx xy - 2x + 6y…

A: We can solve the given differential equation by using the variable separable method.

Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: Given that, y''-9y'+14y=3-ex Now to find the complementary function take, y''-9y'+14y=0. Take m=ddx…

Q: Solve the general solution of the given differential equation by making it exact. 2.)y?dx + (xy-1)dy…

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Q: Solve the given differential equation d' y dy x2 -+ 2x – 12y= x² (ln x) dx² dx

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Q: Find the general solution of the given differential equation. y" - 5y' + 5y = 0

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Q: find the general solution of the given differential equation. 6.y″ + 2y′ + y = 2e−t

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Q: Solve the given differential equation by separation of variables. dy xy + 8y - x - 8 dx xy - 5y + x…

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Q: d²y dy -4. +3y = e²x dx? dx

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Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: We have  d2ydx2-2dydx+y=xe6x-e6x ;  dydx=0 and y=0 when x=0   The given equation can be written as…

Q: Solve the given differential equation (x + 3y – 4) dx + (x + 4y – 5) dy = 0 -

A: We have to solve the given differential eqn:- (x+3y-4) dx + (x+4y-5) dy = 0 Dy/dx = (-x-3y+4) /…

Q: Q2/ Find the general solution and the particular solution for the differential equation: dy xe?y %3D…

A: topic - differential equations

Q: Given the differential equation x d² y dx² 0 and one solution y₁ = A (constant), use reduction of…

A: This question is related to ordinary differential equation.

Q: solve the given differential equation by seperation oF values. dy y xy+4y-* -9 dx xy-Sy tx-5

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Q: Find the particular solution of the differential equation. dy - 4x³ e dx ; y(0) = 9 y =

A: Here I am attaching image so that you understand each and every step.

Q: Solve the given differential equation by separation of variables. xy + 7x - y - 7 xy - 2x + 8y - 16…

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Q: Find the general solution of the given differential equation. (2 +t) y' + y = 1

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Q: (x + 2y – 1)dx + (3x + 6y)dy = 0.

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Q: Find the general solution of the given differential equation. x²y' + xy = 2 y(x)%3D

A: This is a problem related to differential equation. Based on the general formula we will answer the…

Q: Find the particular solution of the differential equation. dy 7 - 7x° e -×' ; y(0) = 4 dx y =

A: See below the answer and calculation

Q: Solve the given differential equation by separation of variables. dy = e5x dx + 6y

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Q: Solve the given differential equation by separation of variables. dy xy + 6y-x-6 = dx xy-7y+x-7

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Q: Find the particular solution to the differential equation d?y = 4e* + 3x² dx2 dy given y = -3 and dx…

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Q: Q1- Find the solution of the following differential equation d²y dy +2+y = 0 dx 4x- dx²

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Q: dy dx ey- 1 y ex y(0) = 2

A: Topic:-  application of integration

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.