Question 2: Solve the following problem with the fourth-order RK method: d?y 2- dx2 dy +3 +3.125y = sin x dx where y(0) = 5 and y(0) = 3. Solve from x = 0 to 5 with h = 0.5. Find the error considering the exact solution is y(x) = e75 (5.292237 cos x + 6.859589 sin x)-0.292237 cosx +0.109589 sin x Display the analytical and numerical results on the same graph.

Q: Solve the following equation: (X² + y²) dx = 8 (XY)dy, and find the value of y at x = 5 where y = 0…

A:

Q: a) Use the d'Alembert solution to solve -00 0, 9 Əx² ' x,

A:

Q: Find the general solutions (implicit or explicit) to the following equations. (a) y' = e3x-2y + x²…

A: First order ordinary differential equation.

Q: 9. Let a=dx 1 Find the value of a + b. and 2π 9 b= sin(6x) dx 【 0

A:

Q: cos(t) dt 2/3sqrt(x+5)^5-10(x+5)^(1/2) +C (5 sin(t) + 9)2

A:

Q: -2t sin(3) + 6t cos ()

A:

Q: Find the smallest positive solution x: (sec(x)+4)(sec(x)+4) = 4

A:

Q: Solve. Soc 3 cos (5xx)dx

A:

Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

A:

Q: Taking into account that x =c₁ cos (1) + ₂ sin (1) is a family of solutions of the equation: x" + x…

A: Consider .We need to show that  is solution of .We need to find solution, if .

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.