Classify each of the equations above as autonomous, separable, linear, homogeneous, Bernoulli, or neither. A. y′= sin(x) + cos(y); B. y′=(y/x)+ 2x/(y+2x); C. y'= (x^2+y)/ln(x) D. y' = e^(x^2+y^2)+e^(x^2-y^2) E. y'= (x^3)y+(Y^3)x

Q: By finding suitable integrating factors, solve the following equations: (a) (1-x?)y' + 2xy…

A: (a) Consider the given equation as equation (1) and obtain the integrating factor as follows.

Q: 1. Find all solutions of y' = x ln x

A:

Q: Choose the correct answer If x2 + y2 = 9, then y'=...  -y/x  y/x  -x/y  x/y

A: We have to find y'

Q: y = eαx sin(βx) find y''

A: Keep these rules in mind while solving the question:   Product rule of differentiation:…

Q: If xy? - y3 = 5, find y'. y' =

A:

Q: of y' = x²/(y + 1)?

A:

Q: 5. Solve the (Riccati) equation in terms of the Airy functions. y' = x - y²

A: Answer :-

Q: 1. Find y'. (a) v5æy + 2y = y² + xy³

A: Differentiate wrt x

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.