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12 cards from this deck
Equations containing derivatives like dydx\frac{dy}{dx}dxdy
Has dydx\frac{dy}{dx}dxdy as highest derivative
Has d2ydx2\frac{d^2y}{dx^2}dx2d2y as highest derivative
Type 1: general, Type 2: initial cond., Type 3: 2nd order
Solution with arbitrary constant of integration
Uses initial conditions to find specific value of c
Separate variables, integrate both sides, rearrange for y
Use initial condition to find c, then substitute back
Let v=dydxv = \frac{dy}{dx}v=dxdy, then dvdx=d2ydx2\frac{dv}{dx} = \frac{d^2y}{dx^2}dxdv=dx2d2y
Get all y terms one side, all x terms other side
lnx+c\ln x + clnx+c
ex+ce^x + cex+c
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