In a nursery, the reason for spreading a virus epidemic is equal to half of those who have not gotten sick yet. if 200 children are enrolled in the nursery, give a differential equation for the number of children infected N with respect to time t in days. Solve the differential equation to answer the following: If a sick  child started the epidemic, will they all be infected three days later?

Q: Solve this separable differential equation. y' = e-(2x – 4). 3.

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Q: a. Classify and solve the first order differential equation y' = /2 +e'.

A: Answer  Linear differential equation is of the form         y'+Py=Q Where P,Q are function of t.

Q: Use undetermined coefficients to solve the differential equation y"" -y=e¹- x + 16.

A: We have given a differential equation ,  y''' - y = ex -x + 16 First we will find complementary…

Q: Solve the differential equation 4x(dxdt)=7, if x=10 when t=0.

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Q: Find the differential equation whose solution is given by: y^2=4ax

A: To find the differential equation for y2=4ax differentiating this equation with respect to x.

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

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Q: Determine whether the following equation is a solution to the corresponding differential equation.

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Q: Solve the differential equation: y = 3x +log P.

A: Given equation is y=3x+log P Let us consider P as a constant and then dydx=ddx(3x + log…

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

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Q: Your answer is correct. Find a differential equation whose general solution is = = C₁e⁹t + c₂e-³t.

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Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-3t 5t = 0

A: The general solution,y=c1e5t+c2e-3t

Q: After t hours, the percentage of alcohol in the blood decays according to the differential equation…

A: After time t=9.555 hours....they can legally drive...for detail solution...go through the solution

Q: In the given question , determine whether the function is a solution of the differential equation…

A: Substitute the value of y in the equation to determine whether the function is a solution to it or…

Q: A city block has 10 pigeons and then 1 week later there are 15 pigeons. Assuming the rate of growth…

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

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: 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: ~2 _ dar,ך3-א 3זר) ד2?ו? .מ

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Q: Find the differential equation that has y = C1 + C2x as its general solution.

A: To find the original differential equation we  have to eleminate the arbitrary constants by…

Q: 3 X' -3 5

A: This question related to system of ode.

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: -y'-11ly 0

A: Given differential equation is y''-y'-11y=0

Q: If = and f(0) =-4, find the particular solution to the differential equation.

A: Given equation,  dydx=x2y and f(0) = -4∫ydy=∫x2dxy22= x33+Cy2 = 23x2+CGiven x=0 , y= -416=0+CC=16y=…

Q: If the rate of change in the microwave rays M(x), where x is the distance, decreases with a rate…

A: This question is about application of differential equation

Q: Find the general solution of the differential equation. 4dy + ydx = x²dy

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Q: Most savings banks advertise that they compound interest continuously, meaning that the amount S(t)…

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

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Q: Solve the given differential equation by undetermined coeff

A: Given,         y''+2y'+y=sin(x)+4cos(2x)            ...(1)

Q: In the given equation , write and find the general solution of the differential equation that models…

A: Consider the given statement, " the rate of change of P with respect to t is proportional to 25-t"…

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: In the given equation , determine whether the differential equation is linear. Explain your…

A: The given equation is 2-y'y=5x................(1)

Q: In the given question , determine whether the statement is true or false. If it is false, explain…

A: If y=fx is a solution of a first-order differential equation, then y=fx+C is also a solution. The…

Q: As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds…

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

A: Given the differential equation :

Q: 12 2. X' = 4 %3D

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Q: Solve the differential equation when = 5(10 – P) if P = 2 when t = 0.

A: Solving the problem by solving the diff equation.

Q: Suppose that the number x(t) (with t in months) of alliga- tors in a swamp satisfies the…

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Q: Solve The Differential Equation Step by Step 4t²x" + (t²+1)x=0

A: Given differential equation is 4t2x''+(t2+1)x=0         (1) Let the solution be x=∑antn+m Then…

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

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Q: 0 0 6. X' =0 3 1 X -1

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Q: (y')³.x – (y')².y – 1 = 0

A: Assume y'=p, write the given equation in terms of y then differentiate the equation with respect to…

Q: Please Find the general solution to the differential equation x'''+x''+x'+x=0

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

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Q: ry? V1+ x²

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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: In a chemical reaction, a compound changes into another compound at a rate proportional to the…

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Q: Solve the differential equation on  Y=xp+p-p3

A: We have to find

Q: 4. x" +x=e+!.

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Q: Find the differential equation whose solution is given by y^2=4ax

A: topic - differential equations

Q: t. t.

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: (1 0 7. X' = |2 2 1 X 0 1

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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.