13. y' +4y = 2, y(1) = 2 %3D

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: The brine is entering more and going out less at rate (3 gal/min -2 gal/min = 1 gal/min), so…

Q: 5. For what values of r does the function y = e™* satisfy the differential equation 2y" + y' – y =…

A: Given , differential equation       2y" + y' - y = 0   (2D2 + D - 1)y = 0 The auxiliary equation of…

Q: 7. Evaluate Soy4 2 - y dy using Gamma/Beta function.

A: The solution is given as

Q: dx dy dz y +z X + y X +2

A:

Q: A radioactive isotope decays at a rate proportional to the amount of the isotope, in other words…

A: Consider the radioactive decay of an isotope is given by  and the solution of this differential…

Q: dy + ycotx = 1 dx 2.

A:

Q: 4. Show that both x₁ (t) = et cost and x2(t) = et sint are solutions to the second-order…

A: To show that both x1t=e-t cos t, and  x2t=e-t sin tare solutions to the second‐order differential…

Q: Determine the particular solution that satisfies the differential equation and initial condition…

A:

Q: 3. Show that the differential equation dx is homogenous. Zxy

A:

Q: 3. What is the difference between a solution of a differentialequation and a solution of an…

A: The solution represents a family of solutions all of which satisfy the system of differential…

Q: Find the differential equation (Family of Curves): Lines with slope equal to the negative reciprocal…

A: Please check step 2 for solution.

Q: (3) y = ln¯' væ

A:

Q: Define in your own words   Differential equation

A: Differential Equation: Any equation which contains derivatives is called the differential equation.…

Q: Explain briefly the classifications of the Differential Equations?

A:

Q: ex 2. y" — 2у' + у %3 1+ x2

A:

Q: 2. Consider the differential equation y' -()y = 2+G) t If y(0) = yo, find the particular solution to…

A: Explanation of the solution is given below...

Q: Is the differential equation x" + e^x - 1 = 0 conservative or non-conservative? Explain why? If it…

A: Given x''+ex-1=0

Q: in differentials of functions, if x change by a small amount dx then, what will happen to y?

A: Let a function be y=fx then here y is the dependent variable and x is the independent variable. The…

Q: In a city of a fixed population of "P" people , the rate of change (with respect to timet) of the…

A: Given Data: A city has a fixed population is P. Also given, the rate of change (with respect to…

Q: ① Solveing dy - - x dx = 。 ㅎ

A:

Q: Suppose a student carrying a flu virus returns to an isolated college campus of 3000 students.…

A: Total no. Of students=3000 And x is the no. Of students interacted with the flu.

Q: 1. What is the integrating factor of the differential equation ydx – xdy = 0 using case 1?

A:

Q: 3. Determine the differential coefficient of y 2x- 3 when x = 3 Give the answer correct to 3…

A:

Q: y ln x - x ln y = 1

A: ylnx-xlny=1Treat y as yx

Q: (b) Find the complete integral of non-linear first partial differential equation Oz. + y = qz.

A:

Q: Assume that the rate of evaporation for water is proportional to the initial amount of water in a…

A: Here, given that rate of change of evaporation is proportional to the initial amount of water.…

Q: Write in your words about some of the applications of the partial differential equations With…

A: Given :- some of the applications of the partial differential equations

Q: A student carrying an influenza virus returns to an isolated college campus with 1,000 students.…

A:

Q: This problem deals with the differential equation dx/dt kx(x – M) – h that models the harvesting of…

A:

Q: What is the particular solution to the differential equation [x+(1+x)y] = 12 with y = 0 and =0 when…

A:

Q: 3. Show that the differential equation zxy

A:

Q: Obtain the differential equation of the family of lines passing through (-1.1).

A:

Q: 3. Obtain the differential equation of the family of straight lines passing through (0.1). SAdd File

A:

Q: What is the solution of the partial differential equation X

A: x∂z∂x+y∂z∂x=z is first order partial differential equation. For solution we use Lagrange's method…

Q: Classify the differential equation 4 4 4 = 0

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: Show that y=x and yex are lenean inde pendent Solution of the Corres pondinp hamogeneous part ot the…

A:

Q: 2. Find the particular solution for the dy differential equation dx = 2xy and y = 3 when x = 0

A: We will find the particular solution of the differential equation , dy/ dx  = 2xy   .

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: To Determine -

Q: Suppose that the population P(t) of a country satisfies the differential equation dP/dt= kP(200 - P)…

A: dPP(200-P)=kdt∫dPP(200-P)=k∫dt1200∫dPP-∫dP200-P=k∫dtInP-In(200-P)=200kt+cInP200-P=200kt+cP200-P=ce20…

Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

A: Given:     Differential equation 2x3-xy2-2y+3dx-x2y+2xdy=0 The differential equation is exact if…

Q: (9))(y– 2x)y' = y %3D

A:

Q: 13. Obtain the differential equation of the family of straight lines at a fixed distance p from

A:

Q: What is the integrating factor for the linear differential equation xy' – 2y = x?

A:

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A:

Q: The amount of a radioactive substance, y, decays exponentially such that its half-life is 8 days. In…

A: topic- differential equations

Q: If the family of curve has 4 arbitrary constants then the corresponding differential equation is c)…

A:

Q: What are two linearly independentsolutions of the differential equation y''-5y'-6y=0

A: We have to find linearly independent solutions of the given differential equation.