1. (a) If y )Fx), and y satisfies the initial conditions y(O)o and y(O) o, show that [Notice that yc)F) and use (10),) (b) Verify that this expression satisfies the prescribed differential equati...
First, verify that y(x) satisfies the given differential equation. Then, determine a value of the constant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition. y' =y+3; y(x) = CeX-3; y(0) = 8 What step should you take to verify that the function is a solution to the given differential equation? O A. Differentiate...
Show if y y(x) is a solution to an autonomous differential equation y' - f(y), then so is any "horizontal translation" of y. That is, show for any real number C, the function yc(x) - y(x C) is also a solution to y'-f . y). Of course, y and yc may have possibly different initial conditions Show if y y(x) is a solution to an autonomous differential equation y' - f(y), then so is any "horizontal translation" of y. That...
In Problems 1 through 10, find a function y = f(x) satisfy. ing the given differential equation and the prescribed initial condition. 1.dy = 2x + 1;y(0) = 3 In Problems 1 through 10, find a function y = f(x) satisfy. ing the given differential equation and the prescribed initial condition. 1.dy = 2x + 1;y(0) = 3
Project. Solve the boundary-value problem: y(1)0 10 Verify that your solution y(x) satisfies the differential equation at every point in (-1,1). Is y twice differentiable at all points in (-1,1)1? Project. Solve the boundary-value problem: y(1)0 10 Verify that your solution y(x) satisfies the differential equation at every point in (-1,1). Is y twice differentiable at all points in (-1,1)1?
Find a function y=f(x) satisfying the given differential equation and the prescribed initial condition. 1 dy dx y(7) = -5 1x + 2
Use Laplace Transforms to solve the differential equation with initial conditions. 16. y' + y=sin x, y(O) = 1.
hellllllllllp please a) Verify that the function y = ?? + is a solution of the differential equation zy' +2y 4x? (x > 0). b) Find the value ofe for which the solution satisfies the initial condition (2) - 5. = Submit Question a) Verify that the function y=x? + с 2 is a solution of the differential equation ry' + 2y = 4x², (x > 0). b) Find the value of c for which the solution satisfies the initial...
5. Find the solution of the differential equation that satisfies the given initial condition dy cos' xsin dx ysin y Yo) - 1. Leave the answer in the implici form. ,y(o)- 1. Leave the answer in the implicit form. 5. Find the solution of the differential equation that satisfies the given initial condition dy cos' xsin dx ysin y Yo) - 1. Leave the answer in the implici form. ,y(o)- 1. Leave the answer in the implicit form.
4. (15pt) Find the solution of the differential equation that satisfies the given initial condition. Show all work and circle your answer. 24% = sec y, y(1) = 4/4
e differential equation y 0 + y = 1 2−x with the initial conditions y(0) = 2. We wish to approximate y(1) using another method. please help me, thanks so much Consider the same differential equation y' +y= with the initial conditions y(0) = 2. We wish to approximate y(1) using another method. (a) Use the method of series to by hand to find the recursion relation that defines y(t) = 2*, QmI" as a solution to this differential equation....