Using Picard’s process of successive approximations, obtain a solution up to the fifth approximation of the equation dy/dx = y + x, such that y = 1 when x = 0. Check your answer by finding the exact particular solution.

Q: if y = 3x2-2x+5 , determine dy/dx using the definition.

A:

Q: dx ex -1

A: Let ex=t ⇒exdx=dt    dx=dtex          =dtt

Q: Differentiate the function. y = (3x- 1)* (4 - x5) 3 dy dx II

A: To differentiate the given function:

Q: Solve =y(2+xy') . =Dy(2+xy") dx

A:

Q: Solve (x² + 1) + 2xy = dy 2 dx x2+1

A: The given equation is;  (x2+1)dy/dx +2xy =2/(x2+1).

Q: Q6// Solve the equation: y cos? x dy + sinx dx = 0.

A:

Q: solve and show steps  dy/dx= 2xy

A: solve and show steps  dy/dx= 2xy

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.