For each of the following differential equations, find the particular solution that satisfies the additional given...

For each of the following differential equations, find the particular solution that satisfies the additional given property (called an initial condition).

y'y = x + 1

Expert Solution

take integration both sides

multiply by 2 both sides

............................where

Colby Messinger answered 3 years ago

Find the general solution of the following differential equations (complementary function + particular solution). Find the...

Find the general solution of the following differential equations (complementary function + particular solution). Find the particular solution by inspection or by (6.18), (6.23), or (6.24). Also find a computer solution and reconcile differences if necessary, noticing especially whether the particular solution is in simplest form [see (6.26) and the discussion after (6.15)]. (D2+2D+17)y = 60e−4x sin 5x

Using variation of parameters, find a particular solution of the given differential equations: a.) 2y" +...

Using variation of parameters, find a particular solution of the given differential equations: a.) 2y" + 3y' - 2y = 25e-2t (answer should be: y(t) = 2e-2t (2e5/2 t - 5t - 2) b.) y" - 2y' + 2y = 6 (answer should be: y = 3 + (-3cos(t) + 3sin(t))et ) Please show work!

Find the particular solution of the first-order linear differential equation for x > 0 that satisfies...

Find the particular solution of the first-order linear differential equation for x > 0 that satisfies the initial condition. (Remember to use absolute values where appropriate.) Differential Equation Initial Condition x dy = (x + y + 7) dx y(1) = 6 y =

Partial Differential Equations (a) Find the general solution to the given partial differential equation and (b)...

Partial Differential Equations (a) Find the general solution to the given partial differential equation and (b) use it to find the solution satisfying the given initial data. Exercise 1. 2∂u ∂x − ∂u ∂y = (x + y)u u(x, x) = e −x 2 Exercise 2. ∂u ∂x = −(2x + y) ∂u ∂y u(0, y) = 1 + y 2 Exercise 3. y ∂u ∂x + x ∂u ∂y = 0 u(x, 0) = x 4 Exercise 4. ∂u...

1.) Let f′(x) = 3x^2 − 8x. Find a particular solution that satisfies the differential equation...

1.) Let f′(x) = 3x^2 − 8x. Find a particular solution that satisfies the differential equation and the initial condition f(1) = 12. 2.) An object moving on a line has a velocity given by v(t) = 3t^2 −4t+6. At time t = 1 the object’s position is s(1) = 2. Find s(t), the object’s position at any time t.

Question

For each of the following differential equations, find the particular solution that satisfies the additional given...

Solutions

Expert Solution

Related Solutions

Find the general solution of the following differential equations (complementary function + particular solution). Find the...

Using variation of parameters, find a particular solution of the given differential equations: a.) 2y" +...

Find the particular solution of the first-order linear differential equation for x > 0 that satisfies...

Partial Differential Equations (a) Find the general solution to the given partial differential equation and (b)...

1.) Let f′(x) = 3x^2 − 8x. Find a particular solution that satisfies the differential equation...

Set up the appropriate form of the particular solution to each of the differential equations below,...

Find a particular solution of the given differential equation. Use a CAS as an aid in...

Use the method of variation of parameters to find a particular solution of the given differential...

Differential Equations Given that ?? = ?? is a solution of the given ODE (a) use...

Determine the form of a particular solution to the following differential equations (do not evaluate coefficients)....