Consider the nonhomogeneous differential equation 1 y" (x) + y(x) = e+ %3D sin x (a) [2 marks] Determine a general solution of the homogeneous equation. (b) [10 marks] Find a particular solution for the nonhomogeneous equation. (c) [2 marks] Solve the nonhomogeneous differential equation.

Q: dy Solve the differential equation = dx = -5x√y. √y = -5x² + Cor y = 0 √y = -5x² + Cor y = 0 2 √y =…

A: Here is the solution:

Q: Solve the differential equation  y(5)+y=sin(x)

A: Given Differential equation is y5+y=sin(x) This is a linear homogeneous differential equation with…

Q: y dy = x(1 + x²)-1/2(1 + y²)/2 dx

A:

Q: Show that the first order differential equation: (3x² cos y + 2x) dx-x³ sin ydy = 0 is not exact,…

A: A differential equation is exact iff

Q: Given an ordinary differential equation in the form: (xy + y² + y)dx – (x + 2y)dy = 0 (Eq. Test the…

A: According to question,Given Differential equation,xy + y2 + y dx - x + 2y dy = 0

Q: Find the particular solution: d³y d²y +2 = dx3 dx² 0 when x = 0, y = -3, y' = 0, y = 12

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.