Separable equations

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Intros
Lessons
  1. Separable Equations Overview
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Examples
Lessons
  1. Separable Equations without Initial Conditions
    Find the general solution of the following differential equations:
    1. 4y3dydx=1x\frac{4}{y^3}\frac{dy}{dx}=\frac{1}{x}
    2. dydx=(1+ex)(y21)\frac{dy}{dx}=(1+e^{-x})(y^2-1)
    3. dydx=(x+2)2xsiny\frac{dy}{dx}=\frac{(x+2)^2}{x \sin y}
    4. dydx=y(3+e2x)\frac{dy}{dx}=y(3+e^{2x})
    5. dydx=exy\frac{dy}{dx}=\frac{e^x}{y}
  2. Initial Value Problems
    Solve the following differential equations:
    1. dydx=xyx\frac{dy}{dx}=xy-x subject to y(0)=2y(0)=2
    2. dydx=x(ex2+4)4y2\frac{dy}{dx}=\frac{x(e^{x^2}+4)}{4y^2} subject to y(0)=1y(0)=1