4. a) Find the general solutions of the following differential equations. Express the general solution in y = f(x) whenever possible. dy x² = dx¯¯_y(1+x²) b) dQ dt =k(Q-70), k is any constant > 0

Q: mine the differential equation function whose general solution is the family 2x y = 1+206**

A: The solution a DE is given byClearly it has one arbitratry constant, hence the DE must be a first…

Q: Q2\ A-Find a general solution of each of the following differential equations :

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: Find the solution to the differential equations xdt = (t³ — 3t) In² xdx

A:

Q: Solve the following differential equations Use variation of parameters. (D²+1) y sec ¹x

A:

Q: Q6. Determine the order, degree and state the linearity of the following differential equations: a)…

A:

Q: Consider the differential equation 4y" – 4y' – 8y = . Find a particular solution for the given…

A: Given differential equation 4y'' - 4y' - 8y = 8ex

Q: y' + (2 tan x)y = - cos'x

A:

Q: Q1 By eliminating the constants A and B from the equation y = Asin 2x + B cos2x, form an ordinary…

A:

Q: 1) y = c x2 2) y = ce* + c2e¬*

A:

Q: 1. Solve the following linear differential equations with constant coefficients:

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: a differential equation is classified as a homogeneous DE if one can directly isolate all functions…

A: A differential equation is classified as a homogeneous DE if one can directly isolate all functions…

Q: ne differential en y(3) =

A:

Q: 1. )Solve the Linear Equation dý Зу + x3 2dx X

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: nd the solution of the differential equation = Z 3 + sin(z) with i dz

A: Given: dfdz=z-23+sin(z)f(0)=2

Q: 2) Find the differential equation by eliminating the arbitrary constants A and B from B y = 5 Ax+ —…

A:

Q: Which of the following equations is NOT a variable separable differential equation? A. 2xydx + (x² +…

A:

Q: QI) Solve the following partial differential equation Ux + Uy = (sec x + sin y). U

A:

Q: * + 6x) dx + ( In x - 2) dy = o 3. (2x y2 + 24) dx + (2x²y+ 2x)dy = 0 2.

A:

Q: Let a,b be constants. The differential equation: x' (t) = ax(t) + b Has the solution: x(t) = xt *…

A:

Q: Find the differential equation of the following function (x + y – 1)dx + (2x + 2y + 1)dy = 0 a. x +…

A: Given differential equation is  (x+y-1)dx+(2x+2y+1)dy=0