Separable Differential Equations

$$3y\cdot dy=\left(2x+1\right)dx$$  

$$\frac{dy}{3y}=\left(2x+1\right)dx$$  

$$\frac{dy}{3y}=\frac{dx}{2x+1}$$  

$$3y^{-1}dy=\left(2x+1\right)dx$$  

$$3\ln\left|y\right|=x^2+x+C$$  

$$\frac{3}{2}y^2dy=x^2+x$$  

$$\frac{3}{2}y^2=x^2+x+C$$  

$$3y^2=\frac{1}{2}x^2+x+C$$  

$$\frac{1}{y}dy=\left(2-x\right)dx$$  

$$y\cdot dy=\left(2-x\right)dx$$  

$$\frac{dy-2y}{y}=xdx$$  

$$\frac{-2y+dy}{y}=x\cdot dx$$  

$$\ln\left(y\right)=x-x^2+C$$  

$$\ln\left|y\right|=2x-\frac{1}{2}x^2+C$$  

$$-\frac{1}{2}y^{-2}=x-\frac{1}{2}x^2+C$$  

$$\ln\left|y\right|=\frac{1}{2}x^2-2x+C$$  

$$e^{-y}dy=e^xdx$$  

$$-\frac{dy}{e^y}=e^xdx$$  

$$\frac{dy}{e^{\left(x+y\right)}}=1dx$$  

$$1dy=e^{\left(x+y\right)}dx$$  

$$e^y=e^x+c$$  

$$e^{-y}=e^x+c$$  

$$-e^{-y}=-e^x+c$$  

$$-e^{-y}=e^x+C$$  

Terrible, I am really bad at it.

Ok, I can kinda do it right sometimes

Good, I am pretty decent and can score 3-4 points per problem

Great, I am very confident and get them all the way correct most of the time.