Suppose that in a certain company, the relationship between the price per unit p of its product and the weekly sales volume y, in thousands of dollars, is given by   dy dp = −  4 5   y p + 9  . Solve this differential equation if  y = 8  when p = $23.

Q: Find a differential equation whose general solution is y = C₁e6t + c₂e-4t y" - 2 y' - 24 = 0 X

A: The solution of the DE is: y=c1e6t+c2e-4t where the solutions to the auxiliary equation are 6 &…

Q: y = ce2t + Cze -3t y = ce-t/2 + cze¯ -2t

A:

Q: What is the particular solution to the differential equation (1-xy)? + (y² + (1-xy)- )dy = 0 and y =…

A: Givendx1-xy2 + y2 + x21-xy2dy = 0withy(4) = 1

Q: The general solution of the differential equation 81.x² y" + 81xy' + (81x² – 25)y = 0 is? Check all…

A:

Q: yー 5y+6y= xex

A:

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

A: Given,  In a certain company, the relationship between the price per unit P and the weekly sale y,…

Q: Solve for the general solution of the below differential equation y" + 8y + 25 0

A: Given the differential equation is y''+8y+25=0. Calculate the general solution of the given…

Q: Verify that the general solution satisfies the differential equation. Then find the particular…

A: We have to solve

Q: For the nonhomogeneous linear differential equation of 2nd order, solve the following y" - 4y – 12y…

A: To solve the given 2nd order homogeneous linear differential equation.

Q: What is the general solution to the the differential equation3y" - y'- 2y = 10e *?

A:

Q: Find the solution of the Linear Homogenous Differential Equation with Constant Cofficients. (D³ +…

A:

Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-2t 2 = 0

A: We need to determine a differential equation corresponding to the general solution: y=c1e5t+c2e-2t.

Q: What will be the order of the differential equation if its solution is y=Acos7x-Bsin7x a. None of…

A: Homogeneous Linear Differential Equation with Constant Coefficients: A homogeneous linear…

Q: What is the order of the differential equation which has a general solution given by y = Ae" + Be2 +…

A:

Q: Show that the given function is a solution to the differential equation y=3x2+1, 2ydx-xdy=2dx

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Q: When à = 0 the differential equation becomes X" = 0 which gives the solution X = ax + b.

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Q: (y – c,)² + (x – c2)² = 1 %3D -

A:

Q: Suppose y=P(t) is the number of a certain type of bacteria on a surface, and P(t) satisfies the…

A:

Q: Find the general solution of the differential equation: xy' + y = 3 + 7x. - Use lower case c for…

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

Q: What is the solution of the following differential equation that satisfies y (1) = 7 and y '(2) = 3?…

A:

Q: Find a differential equation whose general solution is y = c₁est + c₂e-2¹. 5t = 0

A: I have given the answer in the next step. Hope you understand that

Q: Verify that the function y = Ce5x is a solution of the differential equation           y′ = 5y

A: The given function is  y = Ce5x  The differential equation is y′ = 5y

Q: Assume that the number of people y(t) (in million) who have heard the President announcement  to…

A: Given the differential equation :

Q: Solve for the general solution of the differential equation : ( D + 100 ) y = 0

A:

Q: 3. (2xy-x + 2y - 1) dx +(4x²y² - x² + 4xy² -x) dy = 0

A:

Q: What is the differential equation of 2y'=3y+1 when y(1)=0

A: Consider the provided D.E 2y'=3y+1  when y1=0 We need to find the solution of the given D.E, Since,…

Q: (i+ y? tXy?) dr t (x?y ty +2xy) dy

A:

Q: Find the particular solution to the differential equation 3t 4t у + Зу + 3у + у %3D 192е y = 500е -…

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Q: y = cje* + cze²r y" -y – 2y = 0 O 2y " -y' – y = 0

A:

Q: Solve for the Differential Equation m 1. y= -- 7 2. y = Ce-2* + Cze* + 1 3. Ae* + Be-* = Iny

A:

Q: For which value of a is the differential equation (y² + axy³ )dx + (Ky²x² + 2xy) dy = 0 exact

A:

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A: Given: yt=c1et+c2e2t-3tet+cost-e-t2          ...... (1) Solution: Differentiate equation (1) with…

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

A: Let y = emx is the solution to the differential equation, so…

Q: For which value of the constant c is the function y = 15e-® + x + c a solution of the differential…

A:

Q: If the rate of change in the number of cows, W, in a population is proportional to 150 - W(t), where…

A:

Q: If the rate of change in the number of cows, W, in a population is proportional to 150 -W(t), where…

A: We need to solve Differential equation question.

Q: If the general solution of a differential equation is y(t) = Ce-3t + 10, what is the solution that…

A: Given general solution of a differential equation is  y(t)=Ce-3t+10we have to find the solution that…

Q: Find the general solution of the differential equation: 'y'+4 y = x y^(7/2)`. Use lower case 'c for…

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Q: In some chemical reactions, the rate at which the amount of a substance changes with time is…

A:

Q: Solve the first order differential equation. (x3 + y4) dx + 8y3xdy = 0, when x = 4, y = 1/2

A: Explanation of the answer is as follows

Q: Solve the differential equation as follows: (3 + 5x?y³ + 4xy* + 3y³)dx + xy²(3 + 4xy + 3x)dy = 0

A: To solve the differential equation as follows: 3+5x2y3+4xy4+3y3dx+xy2(3+4xy+3x)dy=0

Q: determine the general solution to thegiven differential equation (D2 + 9)3 y = 0.

A:

Q: Eliminate the arbitrary constants to find the differential equation y = C¡e¬* – C2e-2x + Cze-3x

A:

Q: Obtain the differential equation whose general solution is y = C1 + C2 e^.

A: The given general solution is                y= c1+c2e3x We want to find the corresponding…

Q: s, p°+ 3 xp²- yp²-3xyp = 0 find the differential equation

A: Given: p3+3p2−y3p2−3y3p=0 The standard notation for p is p=dydx.

Q: y is related to X through the differential equation: = ax + bx² + cx³ da and y = d when X = 0 where…

A:

Q: Find the general solution of the differential equation: `y+4 y = x y^(7/2)`. Use lower case `c` for…

A: Given problem is :

Q: The differential equation formed from y = Ae3* + Be7ª is: y"-10y'+35Y3D0 y"+12y'+35y%3D0…

A: we have to form the differential equation from the given equation. I have explained in details…

Q: Solve the given differential equation by undetermined coefficients. y" + y" = 8x2 y(x) = %3!

A: The solution is given as

Q: Suppose y=P(t) is the number of a certain type of bacteria on a surface, and P(t) satisfies the…

A: Now,         Suppose y=P(t) is the number of a certain type of bacteria on a surface,          and…

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.