a) Sketch the graph of the solution to the initial value problem. dy/dx = sin x...

a) Sketch the graph of the solution to the initial value problem.

dy/dx = sin x , y(0) = 1

over the interval 0 ≤ x ≤ 4π

b) By finding a suitable antiderivative, evaluate y(2)

Expert Solution

milcah answered 2 years ago

Solve the initial value problem dy/dx = −(2x cos(x^2))y + 6(x^2)e^(− sin(x^2)) , y(0) = −5...

Solve the initial value problem dy/dx = −(2x cos(x^2))y + 6(x^2)e^(− sin(x^2)) , y(0) = −5 Solve the initial value problem dy/dt = (6t^5/(1 + t^6))y + 7(1 + t^6)^2 , y(1) = 8. Find the general solution of dy/dt = (2/t)*y + 3t^2* cos3t

Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y...

Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y Initial conditions: x(0) = 0 y(0) = 2 a) Find the solution to this initial value problem (yes, I know, the text says that the solutions are x(t)= e^3t - e^-t and y(x) = e^3t + e^-t and but I want you to derive these solutions yourself using one of the methods we studied in chapter 4) Work this part out on paper to...

Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 − 2) dy...

Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 − 2) dy = 0, y(1) = 1

Find the general solution of the differential equation (x + 2y) (dx-dy) = dx + dy.

Problem 7. Consider the line integral Z C y sin x dx − cos x dy....

Problem 7. Consider the line integral Z C y sin x dx − cos x dy. (Please show all work) a. Evaluate the line integral, assuming C is the line segment from (0, 1) to (π, −1). b. Show that the vector field F = is conservative, and find a potential function V (x, y). c. Evaluate the line integral where C is any path from (π, −1) to (0, 1).

Question

a) Sketch the graph of the solution to the initial value problem. dy/dx = sin x...

Solutions

Expert Solution

Related Solutions

Solve the initial value problem dy/dx = −(2x cos(x^2))y + 6(x^2)e^(− sin(x^2)) , y(0) = −5...

Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y...

Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 − 2) dy...

Find the general solution of the differential equation (x + 2y) (dx-dy) = dx + dy.

Problem 7. Consider the line integral Z C y sin x dx − cos x dy....

Solve the following initial-value problem: (ye2xy + x)dx − (y2 − xe2xy)dy = 0, y(2) =...

The initial value problem sinx dy/dx-3y = -cos x; y(π) = 0 and has a unique...

Solve the initial value problem dy/dx + H(x)y = e5x ; y(0) = 2 where H(x)...

Solve the given initial-value problem. dx/dt = y − 1 dy/dt = −6x + 2y x(0)...

Find dy/dx by implicit differentiation: cos(x+y)=y^3 sin x