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dydx=f(x,y)\frac{dy}{dx} = f(x, y)dxdy=f(x,y)
Rewrites equation in new variables to simplify and make solvable
Back-substitute original variables
F(x)=e∫P(x) dxF(x) = e^{\int P(x) \, dx}F(x)=e∫P(x)dx
dydx+P(x)y=Q(x)\frac{dy}{dx} + P(x)y = Q(x)dxdy+P(x)y=Q(x)
r′sinθ+rcosθ=0r' \sin \theta + r \cos \theta = 0r′sinθ+rcosθ=0
r′cosθ−rsinθ=0r' \cos \theta - r \sin \theta = 0r′cosθ−rsinθ=0
r′sinθ+rcosθr′cosθ−rsinθ\frac{r'\sin\theta + r\cos\theta}{r'\cos\theta - r\sin\theta}r′cosθ−rsinθr′sinθ+rcosθ
ddx[F(x)y]=F(x)Q(x)\frac{d}{dx}[F(x)y] = F(x)Q(x)dxd[F(x)y]=F(x)Q(x)
A=12∫αβr2 dθA = \frac{1}{2} \int_\alpha^\beta r^2 \, d\thetaA=21∫αβr2dθ
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