> The differential equation dy 7y +6 = -2 has the initial conditions that y = 1 at x 2. %3D dx

Q: Find the particular solution of the differential equation dy 6x° e -x* : y(0) = 3 dx

A: We need to integrate both sides for particular solution

Q: 4. Find the general solution of the differential equation: dy dy + 14y = x? dx %3D dx?

A: d2ydx2-9dydx+14y = x2 Auxillary equation is m2-9m + 14 = 0 m2-2m-7m+14=0 m(m-2)-7(m-2)=0 m=7,2

Q: dy 4cos(2r) and y=- 2 when x=- dx 3x Suppose What is the particular solution to the given…

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Q: Find the particular solution of the differential equation (y + 1)dx – x dy = 0 if x=1 when y=0.

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Q: What is the particular solution to the differential equation dy dx 3y3 with the initial condition…

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Q: dy = 0 ? What is the general solution to the differential equation y dx² dx

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Q: Solve for the general solution of the below differential equation. d²y dy 9. + 24 + 10 = 0 dx2 dx

A: The general solution of the given ODE can be calculated as follows:

Q: Evaluate the given differential equation. dy 4sin2x dx y = 2; x 2

A: To evaluate: The differential equation dydx=4sin2x. Given: The condition for the given differential…

Q: For what value of k does y = 4+ 5ek satisfy the differential equation: dy = 12 – 3y? dx k =

A: Satisfy given equation in differential equation

Q: Solve the differential equation with the given initial condition.

A: Given differential equation is, dydx=4x3, y1=4.   It is simplified as follows: dydx=4x3dy=4x3dx…

Q: 2. Find the general solution of the differential equation: dy ip 5 + 6y = e ,3x - dx? d.x

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Q: solve the differential equation with the given initial condition.

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Q: Find the general solution of the differential equation dy/dx = (ex + 5)2

A: dydx= (ex+5)2 dydx=e2x+10ex+25dy = e2x+10ex+25dx

Q: dy 5x - (c) satisfies y(0) = 7. Find the particular solution to the differential equation xy that dx

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Q: dy = 4sin( 2x) and y=2 when *x= dx Suppose What is the particular solution to the given differential…

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Q: With initial values y(0)= y'(0) = 1, the solution of the differential equation d'y dx? dy +4- + 4y =…

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Q: The differential equation 2x+ 1+xy? dx+ -2y+ dy 1+xy, is exact. O True O False

A: Given that the given differential equation is exact. We need to check whether it is True or False.

Q: Given the differential equation: dy _ 2 x + 1 1 y With initial conditions: y(-3)=9 dx Calculate its…

A: Solution: The objective is to find the solution to the given differential equation

Q: dy 2) x- - 1 = -2e-y 1 = dx

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Q: For what value of k does y = 4 + 5ek* satisfy the differential equation: dy = 8 – 2y? dx k =

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Q: d²y What is the particular solution to the differential equation x dx? dy x² with y = 0 and dy = 1…

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Q: Given the differential equation y²dx + (3xy + y² − 1) dy = 0 What is value of SM ? dy

A: Given the differential equation, y2 dx+3xy+y2-1 dy=0To find the value of δMδy.

Q: Given the differential equation dy + 4y = 5x dx

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Q: Find the general solution of the differential equation given below ylnxlnydx + dy = 0

A: We will solve it using separating the variables

Q: 3. Find the general solution of the differential equation: dy dy 5 + 6y = e2r - dx? dr

A: Given differential equation       D2-5D+6=e2x

Q: In the differential equation (6x - 3y + 2)dx-(2x - y - 1)dy = 0 , we let the substitution dx =…

A: Please see the answer below.

Q: Find the general solution for the differential equation dy/dx=y2(1+ex)

A: the given differential equation is: we have to find the general solution for the given differential…

Q: What value of k would make the differential equation dx uy + In(x + 1) = a*y* variables separable?…

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Q: State the order of the given ordinary differential equation. d3y dy 4 + y = 0 dx3 dx

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

Q: (d). Consider the differential equation dy Vy? + 1, x > 0 with y(2) = 0. Show that the solution of…

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Q: What is the long-term behaviour of the general solution to the differential equation dy = 5(1 – y)…

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Q: dy 1. Verify y =x* is a solution to the differential equation 2 = xy dx 16

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Solve the differential equation dy/dx = 5y2/sqrt(x) Initial condition: y(9) = 1/20 Therefore y(x)…

A: First, we separate the variables dydx=5y2xdyy2=5dxxy-2dy=5x-12dx

Q: 4) y = 2xy' – Iny' Find the general solution of the differential equation. %3D |

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Q: Solve the differential equation dy (y ¹6 x) 1+x. dx Use the initial condition y(1) = 5. 17 Express…

A: This question is related to differential equations, we will solve it using given information.

Q: 1. Find the general solution of the differential equation: dy, dy + dx3 dºy dy = 0 dx6 dr5 dx?

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Q: dy = 1 + y/x dx

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Q: Solve the non-homogenous differential equation below dy 2y + x – 3 dx y+ 2х —3

A: Given that a non homogeneous differential equations and we solve by using general property of…

Q: dy Q2/ Find the general solution to the differential equation 2x+9y-10 %3D dx 6х+2у-10

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Q: Find the general solution of the differential equation. dy = xy + 3x dx

A: To find the general solution of the following differential equation.dydx=xy+3x

Q: In the differential equation (6x – 3y +2)dx-(2x – y-1)dy=0, we let the substitution dx =

A: Given differential equations is non homogeneous differential equation.. We have to find the…

Q: dy 2xy%=D0

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Q: Find the particular solution of the differential equation dy +4y x dx if y = 0 and x=1.

A: We have to find the particular solution of the differential equation xdydx+4y=x3  if y=0 and x=1.

Q: Find the Particular solution of the differential equation (dy/dx) - 3y/x =(x cubed); if y(1) =4.

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Q: 2. Find the general solution of the differential equation: dy dy 5 + 6y = e3x dx - dx?

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Q: 4. Find the general solution of the differential equation: dy dy 9- dr + 14y = r dr?

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Q: In the differential equation 4(3x+ y– 2)dx– (3x+ y)dy = 0, we let the substitution dw=

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Q: 2. Find the general solution of the differential equation: dy 52 + 6y = e2r dx? dx

A: Solution is given below:

Q: the differential equation ( + 6x)dx + (Inx – 2)dy = 0 is exact - Select one: O True O False

A: The given differential equation is yx+6xdx+(lnx-2)dy=0 We have to check whether this differential…

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.