4. Find the solution of the given initial value problem. 2 y + -y cos t -, y(1) = 0, t > 0 12

Q: y" + 2y' = 4x – 5 cos(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: b. Solve the initial value problem: f (x)= sin x +e2, f(0) = 4 1 f (0) 2

A: Given: f''(x) = sin x + e2x, f(0) = 14 and f'(0) =12

Q: c) Solve the initial value problem (1 + cos² t). 21) dx dt - x sin 2t = 4t² + 5t +4, x(0) = 2

A:

Q: 3y? dy dx cos(пх)" o Consider the differential equation Let y = f(x) be the particular solution to…

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: Use variation of parameters to find a particular solution, given the solutions y₁, y2 of the…

A:

Q: dy Solve the initial value problem: 4( sin(t)- + cos(t)y dt = cos(t) sin (t), 0 < t < T, y(T/2) =…

A: Here the first order differential equation is given as: 4sinty' +costy=cost⋅sin7t0&lt;t&lt;π,…

Q: Solve the separable differential equation Subject to the initial condition: y(0) = 4. y = 8x - 6y√x²…

A:

Q: y′′+ 4y = 32t cos 2t, y(0) = 0, y′(0) = 2

A:

Q: u" (x) = – sin(x), 0 < x < T, u(0) = u(7) = 0.

A:

Q: (5) Solve the IVP:dy - y = e* cos(2x), y(0) = 2 dx

A:

Q: Find the implicit solution of the differential equation (1+sin(y))dx + (1+x cos(y))dy = 0.

A:

Q: v(t) = 3 sin(t) – 4 cos(t); s(0) = ( - s(t) =

A: to find the value of s(t)

Q: Q4. Simplify the following expression: 3-5 x 39 Click on image to enlarge if needed 12 81 243 324

A: To evaluate :- 3-5 * 39

Q: Find the general solution to / + (xy)² = y²e%* .

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: The number of houses that can be served by a water pipe varies directly as the square of the…

A: Given that, The number of houses that can be served by a water pipe varies directly as the square of…

Q: dy +y=(x-1)y' dx

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.