General & Particular Solutions
Slope Fields, Etc.
Integration by Parts (maybe)
Partial Fractions (maybe)
Integration Potluck
Ski Lifts
100
This is the general solution to \frac{dy}{dx}=y
What is y=Ce^x ?
100
Of dy/dx=x(y-1) , dy/dx=x/y-1 , dy/dx=-x(y-1) , or dy/dx=\frac{x}{y-1} , this is its slope field. 
What is dy/dx=x(y-1)
100
This is \intxe^xdx
What is xe^x-e^x+C ?
100
This is \int\frac{1}{x^2-1}dx
What is 1/2ln|\frac{x-1}{x+1}|+C ?
100
This is the value of \int_0^3\sqrt{9-x^2}dx
What is \frac{9\pi}{4} ?
100
This Bogus Basin chair, historically open only weekends prior to 2024-2025, was recently converted from a fixed double to a fixed quad, might make you make a scrunchy face while picking potatos, carrots, or maybe onions.
What is the Bitterroot Chair?
200
This is the general solution to \frac{dy}{dx}=xe^x
What is y=xe^x-e^x+C ?
200
Of dy/dx=-\frac{x-2}{y} , dy/dx=-\frac{y}{(x-2)^2} , or dy/dx=(x-2)y^2 , this is its slope field.
What is dy/dx=-\frac{y}{(x-2)^2} ?
200
This is \intx\sqrt{x}dx
What is \frac{2}{5}x^{5/2}+C ?
200
This \int\frac{x^2+1}{x}dx
What is 1/2x^2+lnx+C ?
200
This is the value of \int_1^2e^lnxdx
What is 3/2 ?
200
This Bogus Basin lift, serving primarily beginner terrain, was named for Bill "Coach" Everts.
What is the Coach Lift?
300
This is the particular solution to \frac{dy}{dx}=ln(x) with an initial condition of (1,0).
What is y=xlnx-x+1 ?
300
This is a tangent line equation for dy/dx=3x/y for x=1 and y=-6 .
What is y+6=-1/2(x-1) ?
300
This is \intxcosxdx
What is xsinx+cosx+C ?
300
This is \int\frac{1}{1+x^2}dx
What is \arctanx+C ?
300
This is \intx(x^2-3)dx
What is 1/4x^4-3/2x^2+C
300
This Grand Targhee lift did not escort Lewis & Clark to the Pacific, but still ...
What is the Sacajawea Lift?
400
This is the particular solution to dy/dx=9+y^2 with initial condition (0,\sqrt{3})
What is 1/3tan^-1\frac{y}{3}=x+\pi/9 ?
400
This is an approximate value for f(2) using Euler's Method with the initial condition f(1)=7 and dy/dx=y-x with two equal steps.
What is 14.25?
400
This is \intlnxdx
What is x(lnx-1)+C ?
400
This is \int\frac{x}{x^2+1}dx
What is 1/2ln(x^2+1)+C ?
400
This is \intsec(2x)tan(2x)dx
What is 1/2sec(2x)+C ?
400
This Brundage Mountain lift is named for the nirvana we all seek - sunny days playing in powder.
What is the Bluebird Lift?
500
This is an explicit form of the particular solution to dy/dx=x(y+5) with initial condition (0,-10)
What is y=-5e^{\frac{1}{2}x^2}-5 ?
500
For dy/dx=x+sin(y) , this is the rate at which dy/dx is changing when x=1 and y=pi
What is zero?
500
This is \int2sinxcosxdx
What is -\frac{1}{2}cos(2x)+C ?
500
This is -\int\frac{9}{2x^2+11x+5}dx
What is ln\abs{\frac{x+5}{2x+1}}+C ?
500
This is \int_0^3\sin(pi/6x)dx
What is 6/pi ?
500
The world's first lift opened in Sun Valley, Idaho in 1936, and was inspired by systems for loading this tropical fruit onto ships.
What are bananas?