a) Consider the first order differential equation (+²¹² + 1) dy-0 ry'dr + By multiplying the equation with integrating factor = show that the differential equation is exact. Hence, solve the differential equation. b) Find the solution of the following Bernoulli equation dy da +2y = 2y³z. c) The amount r(t) of ethanol in a draining tank changes with time t, given by the differential equation Find r(t) if x(0) = 10. da + 1 30+ t

Q: Solve by applying "Differential Equation using Substitution Suggested by the Equation"…

A:

Q: Solve the differential equation by using an integrating factor: y+(4+2) y = 0, y(1) m 9

A:

Q: ) 2 xýt 2xy - Sinh (32)

A: As per the guidelines I am answering only one question at a time. A differential equation of the…

Q: Solve by applying "Differential Equation using Substitution Suggested by the Equation" (2x + y)dx–…

A:

Q: Solve by the method of: Exact differential equations and integrating factor xy + y² dx + x² + 3xy dy…

A: To solve given differential equations, let us first find the integrating factor which will make it…

Q: Determine the solution of the 1st Ordered Differential Equation: (x - y)(4x + y)dx + x(5x - y)dy = 0

A: We have to solve given problem:

Q: Evaluate the general Solution to the differential equation: Cy-cos-x)dx+ cosxody A y(secx + tan x) t…

A:

Q: Determine whether the differential equation (8x² − 2xy + 6) dx + (2y² − x² + 8) dy = 0 is exact. If…

A:

Q: 2. Solve the differential equation y" + 3y csc V3x

A:

Q: Given the DE as 2xy² + 4 = 2(3 − x²y)y'.

A:

Q: differential equation is given as

A: In this question, the concept of the differential equation is applied. Differential equation A…

Q: x" (t) + x'(t) – 6x = te-tcos2t %3D

A: We use the method of undetermined coefficients to find the particular solution.

Q: Solve the differential equation by the method of integrating factors. y + 7y = cos (e7*) y = Use "C"…

A:

Q: Determine the solution of the 1st Ordered Differential Equation: (x - y)(4x + y)dx + x(5x - y)dy = 0

A:

Q: Determine the differential equation that is satisfied by x(t) = c,e3t + cze¬t – te-t

A:

Q: (D² + 1)y = sec³ x.

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Solve the differential equation , where y, is known solution dy = 2x + dx y-2y, Y = x.

A: Given differential equation dydx=2x2+1xy−2y2......1 This equation is a Riccati  equation. Compare…

Q: dy (2y+re (2y+xe*V)=-(1+ye™Y)

A:

Q: Use order reduction to find the solution of the differential equation. 4x²y"+y= 0; y, = x² In x 1/2

A: Let y1(x) be non-trivial solution of differential equation y''+p(x)y'+q(x)y=0 and let…