Transform into Bernoullis' form the differential equation 2r y' = y (y² + 3x²) %3D dy 3..3 dr * (*) = 'y* dy 'y = y 3 3r 'y = a 'y

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: 4. The Bernoulli's form of the differential equation x'dy+ (2xy-y')dx=0 is

A: Given problem:- The Bernoulli's form of the differential equation x2 dy + (2xy - y3)dx = 0

Q: Using h = 0.2, approximate the value of y(2) for the given differential equation using 4th order…

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Q: (b) Form the differential equation by eliminating the arbitrary constants a,b from y = aez + be 8z

A: Differentiate twice with respect to x then we get the answer

Q: The Bernoulli's form of the differential equation 2x³dy-− y(y² + 3x² ]dx = 0 is

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: Find a particular solution Y of the nonhomogeneous differential equation y 00 + y 0 + y = 2 cost −…

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Q: Find the general solution of the first-order linear differential equation. y + y = 16 cos (x)…

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Q: dy + ycotx = 1 dx 2.

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Q: Generate the values of y for the differential equation   y - x + x*y = dy/dx   For the interval…

A: In this second-order Runga Kutta method, we have to compute k1 using initial conditions then after…

Q: Find the particular solution of the differential equation = 10y sin(x) using the given boundary…

A: To find the particular solution of the given differential equations

Q: Consider the differential equation y' = x+ y. Use Euler's method with Ax = 0.1 to estimate y when x…

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Q: 9. From the differential equation sinh 2x, sketch some of the family of curves. %3D dx

A: Given differential equation, dydx=sinh(2x)dydx=e2x-e-2x2∫dy=∫e2x-e-2x2dxy=e2x+e-2x4+C

Q: find solution of order differential equation  dy/dx=cos2(x-y+1)

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Q: An object of mass m falls from rest and its velocity v given by dv =mg - kv v(0) =0 dt -- where k is…

A: Consider the given equation. mdvdt=mg-kv Further, simplify and make for integration.…

Q: Consider a very large tank filled with 200 liters of fresh water at time t = 0. Suppose that brine…

A: The initial conditions we have are  Initially, tank has 200 litres of freshwater. i.e.  V(t=0) = 200…

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: The solution of the given differential equation for y(1.5) is h=0.1 interval value. Calculate by…

A: Euler's method uses the formula, yn+1=yn+hf(xn,yn) to perform the iterations.

Q: Solve Bernoulli differential equation of y' + xy= ry². %3D

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Q: Determine the solution for the differential equation ry = In(x) for which Y(1)

A: y^2 = (ln x)^2  + 2 ln C

Q: What is the particular solution to the differential equation +1+y = 2e- with y = 1, 2=-1 when x = 0?…

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Q: A first order Bernoum's differential equation is in the form 2. The Bernoulli's form of the…

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Q: Use Euler's Method to find a numerical solution of the differential equation dy y 3+ dx With initial…

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Q: Use separation of variables to find the general solution of the differential equation. 6 cos(tx) xp

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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: Find the general solution for the second-order differential equation ¨y + 8 ˙y − 9y = −3 with…

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Q: (2 + tan2x)(1+е"У)dx — е У tan x dy %3D 0 = 0 %3D

A: Given differential equation is 2+tan2x1+e-ydx - e-ytan x dy = 0,   yπ2=0

Q: Use separation of

A: Given,                     7dydθ=eysin2θysecθ.

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

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

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Q: The differential equation y' – y = 0 has a solution of 1 y(x) = n! n=0 Show v(r) is a soluution to…

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Q: A population (in thousands) grows according to the differential equation dy e ky(L-y), where the…

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Q: The nature of the equilibrium value at y = 3 for the differential equation y = (y – 3) is Stable O…

A: Considering the equilibria at y=3, we see that: For values y<3, we get y'<0 and For values…

Q: A large corporation starts at time t = 0 to invest part of its receipts continuously at a rate of P…

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Q: 2. y" + 4y' + 5y = cos(x)

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Q: The solution of the first order linear differential equation y' + ycotx = cosx is O…

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Q: Particular Integral for the differential equation (D² + 25)y =(cos5x) is given by a. -xsin5x 5 b.…

A: Option; b is correct.  Given differential equation ; (D2  + 25 )y  = cos5x Let D = m; Auxiliary…

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

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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: 7: From an integral equation corresponding to the differential equation d²y dx² dy - sin x- +exy = x…

A: What is Integral Equation: Like differential equation, there is also integral equation. In integral…

Q: What form of the particular solution is appropriate for the differential equationy'' - y'=4+4e*.

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Q: What is a particular solution to the differential equation 2y dx – 3x dy = 0 when x = 1 and y = 1?…

A: This is Separable differential equation

Q: From the differential equation by eliminating the arbitary constant A and B from the equation y = e*…

A: The objective is to form the differential equation by eliminating the arbitrary constant A and B…

Q: 3. The Bernoulli's form of the differential equation x³ydx+(3x¹-y³dy=0 is

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Q: 3. (cosy + ycosx)dx + (sinx – xsiny)dy = 0

A: Given: cosy +ycosxdx +sinx-xsinydy =0 ⇒cosydx +ycosxdx +sinxdy-xsinydy =0

Q: The population y(t) of a certain microorganism grows continuously and quadrupling time is found to…

A: In this question, the concept of the derivative is applied. Derivative We can use a derivative to…

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin æ +…

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Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = aeª +…

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Q: 4. Obtain the Differential Equation from the family of curves of the form y = xC

A: To form a differential equation from given family of curves. Differentiate given family of curves…

Q: Use Teller's method to Solve the differential equation y-X JJ when h=0-2 s y(1)=2 Use The fifth rank…

A: We can solve this using Taylor method

Q: dx + dt? dx +x = 2 dt x, dt6 dt3 = of this differential equation is 9, help (numbers) tion is Choose

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