QUESTION 5 d?y dy a) Solve the differential equation 2 +y%3D5×+3. dx2 dx b) Greenland had a population of 55000 in 1980 and a population of 78000 in 1990. Assume that the rate of population growth is proportional to its population at any time t. Calculate the population of Greenland in the year 2020. c) A hard-boiled egg at 98°C is put under a constant temperature 18°C running water to cool. After 5 minutes, the egg's temperature is found to be at 38°C. Calculate the time taken for the egg's temperature to reach 20°C. [Hint: Use Newton's Law of Cooling]

Q: Which of the differential equation has order 3 and degree 2? option I: (d² dæ? dy + 2- dr - 3 = 5xy?…

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Q: dw + 5e*" = 0 dt 6. Solve the differential equation. 4-

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Q: dy 4. (a) Find the general solution for the differential equation 3- %3D de 4

A: a. given :

Q: The solution of the differential equation below is dy = ky dx %3D

A: Solve the differential equation dy/dx=ky

Q: y – 18y"'+ 81y'= 0

A:

Q: Question 2 Given a differential equation as d²y dy 2². - -3x- +3y=0. dx² dx By using substitution of…

A: Let's solve diffrential equation by using substitution x=e^t  or t=ln(x).

Q: Question 3 Use the method of variation of parameters to solve for the differential equation y" – 6y…

A: The solution is given as

Q: con ver the Following differential equation into a Perfect equation and then find its general…

A: The objective is to convert the given differential equation into a perfect equation and then find…

Q: У(4х + у)dx — 2(х - у)dy %3D0

A:

Q: QUESTION 2 a) Solve the following differential equation by separation of variables method. 2.xydx +…

A: Given; a) 2xydx+(1+3y2 )dy=0 b)dy/dx +3x2y=6x2.

Q: using linear differential equation of order one.

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: (Dª – D³ – 3D² + D + 2)y = 0

A: Explanation of the answer is as follows

Q: 3D4 The solution of the differential equation yy"= 4 is Select the correct answer.

A: Here the ordinary differential equation is given as: y'y''=4Let v=y'⇒v'=y''vv'=4

Q: QUESTION 3 3.1 The displacement X, in t seconds, of a body in damped mechanical system, with no…

A: This is the integration we used during question solving.

Q: Question 7 Determine whether the given differential equation is exact. If it is exact, solve it. dy…

A: First make this equation in the form of Mdx+Ndy=0 then find dM/dy and dN/dx   and if both are equal…

Q: Solve the differential equation given below. dy = 2(-2 – y) dx

A: Given equation; dy/dx = 2(-2 - y)

Q: If the differential equation ydx+xdy= 0 is being solved, what is the geometrical figure represented…

A: Differential equations

Q: 1. Solve the differential equation zy ) dz = dy. %3D

A: Solution of the given differential equation has done here.  See the fig.

Q: Question 19 SM Given the differential equation y dx + (3xy + y² - 1) dy = 0, What is value of dy 00…

A: As we know that; The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. And The Power…

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

A: The solution is given as

Q: In the process of solving the differential equation dy xy dx using the separable method, we get:

A: Consider the following differential equation: dydx=xy1ydy=xdx Integrate the above equation:…

Q: (a) Solve the second order differential equation below: d?y dy - 7 +10y = 4e3x dx dx?

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: Solve the given differential equation (D -3D+2)y=xe* +sin2x

A: We will find out the required solution.

Q: The solution of the differential equation below is dy 3y- + 4x = 0 dx %3D

A:

Q: (D² + 3D – 4)y = 18 e2×.

A: Complete solution of differential equation is :  Y = CF +PI

Q: dw 1. Solve the differential equation 4 = -5e+w dt

A: 4dwdt=-5et+w4dwdt=-5(et*ew)4dwew=-5etdt4 e-wdw=-5etdt

Q: Question 3 dy Solve the linear differential equation, (1+x) +y= cosx, which satisfies the dx (a)…

A: Linear differential equation

Q: Question 1. Find explicit general solution of the following differential equation. dy +y = 10V. 211r…

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Q: Зу" + 2/ — 1у 3D 11? — 1t + 4e 2, Yp =

A: Given

Q: Question 15 A tank contains 6L (liters) of water in which is dissolved 32 g (grams) of a chemical. A…

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

Q: QUESTION 14 solve the differential equation using L.T y" +4y'-5y te' y(0) = 1. y'(0) = 0

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Q: + ху %3D ху"1, у (0) — 3 dx

A:

Q: Consider the situation depicted in Figure 2, in which an object is placed in a room whose…

A: According to the given information, it is required to solve the given differential equation.

Q: (x*y- xy")(xdy + ydx) + dy = 2xdx

A: To solve the differential equation we use some special form

Q: 1 dP Solve the differential equation 1 -- t dt t2

A: Let us consider the given differential equation dydx+P(x)y=Q(x).  Simplify the equation using the…

Q: Solve the differential equation dy 1 dx Зу? by the method of separating the variables.

A:

Q: Solve the given differential equation by separation of variables. dP/dt = P - P^2

A: Solve the given differential equation by separation of variables. dP/dt = P - P^2

Q: (D³ + 3D² – 4D – 12)y = 0

A: To solve the given differential equation.D3+3D2-4D-12y=0

Q: Solve the given differential equation by separation of variables. dy exy e-Y + e-4x - y xp

A: Given the separation differential equation : exydydx = e-y + e-4x-y exy dydx = e-y + e-4x  .e-yexy…

Q: Question # 02 Solve the homogeneous differential equation using substitution method. 1) (y² – xy) dx…

A: given,

Q: Solve this differential equation: dy 0.07y(200 -)

A: Rearrange the given differential equation with the separation of the terms of y, t.…

Q: B. (1+ e2º). "). dr + 2r e20.do = 0

A: Solution:Given Differential equation is                         (1+e2θ) dr + 2r e2θ dθ =0

Q: dy Зх+у-1 dx бх+2у-3

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Q: dy = 6. Solve the differential equation 3y² dz

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: The given exact differential equation is 7x+5ydx+5x-8y3dy=0. Solve the given exact differential…

Q: Question 2 Determine the solution of the second-order differential equation: d'y dy dx2 -7-+12y=e-10…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: