In differential equations the initial condition is used to solve for the _________.
What is the c value?
100
Anti-derivative of x(sin(6x)) dx =
What is (-x/6)cos(6x)+(1/36)sin(6x)+c?
100
In a Euler's Method problem M=______?
What is dy/dy or the slope?
200
integral from (-3) to (-1) of (1/x^2-1/x^3) dx
What is 10/9?
200
Anti-derivative of x^3-7x+1 dx
What is (1/4)(x^4)-(7/2)(x^2)+x+c?
200
Don't solve, but separate the differential equation: dy/dx=(xy/2)
What is dy/y=(1/2)x dx or 2dy/y= x dx?
200
Anti-derivative of sin^3(x)cos(x) dx
What is (1/4)(sin^4(x)) + c
200
In a Euler's Method Problem L=_____?
What is y+M(delta(x))
300
integral from 1 to 4 (1/sqrt(x) dx)
What is 2?
300
Anti-derivative of 2/(x^2-x-6)
What is (2/5)ln(x-3)-(2/5)ln(x+2)+c?
300
Solve dy/dx=1-y for y=f(x) given f(1)=0.
What is y=1-e^-(x-1)
300
What is the first part of the FTC?
What is if f is continuous on the interval [a,b] and F is the anti-derivative of f on [a,b], the the integral from a to b of f(x) dx = F(b)-F(a)
300
Consider the differential equation dy/dx=1-y with y=f(x) the solution. Use Euler's Method, starting at x=1 with to steps of equal size to approximate f(0) given f(1)=0
What is f(0) is approximately -1.25?
400
(d)/(dx)( integral from 0^(sin(x)) of (t^3 dt))
What is sin^3(x)cos(x)?
400
Anti-derivative of x^2(lnx) dx
What is (x^3/3)(lnx) - (1/9)(x^3) +c
400
Solve dy/dx=-3xy, give f(1)=4
What is y=e^((-3/2)(x^2)+(3/2)+ln(4)
400
If F(x)= integral from 1 to 2x of dt/(1-t^3), then F'(t)=
What is 2/(1-8x^3)?
400
Fi?nd the ?first three approximations of y' = y + 1; y(0) = 1 with step size of 0.1
What is y1=1.2 and y2=1.42
500
d/dx( integral from (x^2) to (4 x) of (cos(t) dt))
What is 4 cos(4 x)-2 x cos(x^2)?
500
Anti-derivative of sin^-1(x) dx
*hint: integration by parts
What is xsin^-1(x)+sqrt(1+ x^2) +c
500
Solve dy/dx=xy^3, given f(1)=2
What is y=sqrt(4/((-4x^2)+5))
500
Solve. The integral from 2 to 3 of 3/(x-1)(x+2) dx=
What is ln(8/5)
500
f'(x)= (1+e^x)/(x^2). Use Euler's Method, starting at x=3 with a step size of 0.05, to approximate f(3.1). Given f(3)=6