The differential equation d?y + 10 + 21y = 0 has characteristic equation da = 0 help (numbers) with roots help (numbers) Therefore there are two fundamental solutions help (formulas) Note: Enter the solutions as a comma separated list. Use these to solve the initial value problem d?y dy dy dx + 21y = 0, (0) = 1 dx + 10- y(0) = –1, dx? y(x) : help (formulas)

Q: Find the differential of each function: (a) y =(x' -3)* (b) y= V1-

A: Solution of this question is

Q: Find the general solution of the differential equation and check the result by differentiation. dy =…

A:

Q: Solve dx- dy

A: Here we can use variable separable method to solve the given differential equation. This method is…

Q: (x²+y)dx + dy 0

A: This linear differential equation

Q: (d) Find an equation for each of the graphs: For graph (1), x(t) = For graph (2), x(t) = = For graph…

A: To find the equations of the given graphs

Q: Solve the exact differential equation (x* + y)dx +(3xy +1)dy = 0

A:

Q: 3. Solve differential equation y" - 3y + 4y = 0.

A:

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.