Solve the following differential equation with the given initial condition: (1-t^2) dy/dt = 2t, y=0 when t=0, for -1< t < 1
Solve the following differential equation with the given initial condition: (1-t^2) dy/dt = 2t, y=0 when t=0, for -1< t < 1
ignoring resistance, a sailboat starting from rest accelerates (dv/dt) at a rate proportional to the difference between the velocities of the wind and the boat. a) the wind is blowing at...
Find the radius of convergence and the interval of convergence for: Σ (n=1 to infinity) (2^n(x-2)^n)/(n+2)! Nothing really beyond what the question asks. I think I am supposed to find the...
I have been very stuck on this problem for a few days. I manage to separate the variables however and integrate for y but I am left with a very difficult integral for x.
Find the stability of this differential equation and explain if it's stable or unstable dy/dt = (1-y)(y+3)
I got stuck
I have tried all methods but nothing works.. Thank you in advance
How do I solve the differential equation y'(x)+2y(x)/x=6, when y(x0)=y0; x0=-2 and y0=-4.
How can i get this?
given in series circuit L=1H, R=110ohm, C=0.001F, v=90V. Find the resultant current when the switch is originally open and it is closed for 1s. then it is open again when t=1. use laplace transform...
find the particular solution of the differential equation f"(x)=6(x-1) whose graph passes through the point (2,1) and is tangent to the line 3x-y-=0 at that point
The process I was taught in class was as follows: 1. Transform the second order non homogeneous DE into a system of first order DE. 2. Solve the homogeneous part. 3. Assume the solution...
Attached is the problem from my text book. I'm confused about what I'm actually solving and how to use what I know. I know that Current for the inductor is given by the equation di/dt = v/L and the...
Suppose that an initial population of 10,000 bacteria grows exponentially at a rate of 2% per hour and that y=y(t) is the number of bacteria present t hours later. a) Find an initial-value...
how do you find the second derivative of y=e-x^2
A differential equation is an equation involving a function and one or more of its derivatives. Determine whether the function y=πsinθ+2πcosθ is a solution to the differential equation d^2y/dθ^2...
Answer: c1cos(t) + c2sin(t) -1/3tcos(2t) -5/9sin(2t) Please show the work step by step.
Answer: c1e^-t + c2e^-t/2 + t^2 +6t + 14 -3/10sin(t) - 9/10cos(t) Please show the work step by step.
Answer: c1e^-t + c2t^-t + t^2e^-t
consider the equation f(x)=-6-1 and g(x)=4x^2 select the solution for (fg)(x)