2.4: Separable Differential Equations
( \newcommand{\kernel}{\mathrm{null}\,}\)
A differential equation is called separable if it can be written as
f(y)dy=g(x)dx.
To solve a separable differential equation
- Get all the y's on the left hand side of the equation and all of the x's on the right hand side.
- Integrate both sides.
- Plug in the boundary conditions (e.g. given initial values) to find the constant of integration (C).
- Solve for y.
Solve dydx=y(3−x) with y(0)=5.
Solution
dyy=(3−x)dx∫dyy=∫(3−x)dxlny=3x−x22+Cln5=0+0+CC=ln5y=e3x−x22+ln5y=e3x−x22eln5=5e3x−x22
- dydx=xy with y(0)=1
- dydx=x(x+1) with y(1)=1
- 2xy+dydx=x with y(0)=2
Contributors and Attributions
- Larry Green (Lake Tahoe Community College)
Integrated by Justin Marshall.