Transcription of Differential Equations Summary - a-levelmaths.com
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Differential Equations Summary - a-levelmaths.com
Differential Equations Summary 1. First order Differential Equations a. Variables Separable DE: Arrange through manipulation such that the form below is achieved: dyygdxxf)()(= Integrate subsequently to yield the required solution. Example: Solve ydxdy =1 for y<1. SOLUTIO : 1111= =dxdyyydxdy = dxdyy11 Cxy+= |1|ln Since ,1<y ()Cxy+= 1ln Bxey+ = 1 xAey =1 where BeA=, cB = (shown) This solution is commonly termed the GE ERAL SOLUTIO , where A is unknown. When initial conditions are provided, eg y=0 when x=0, then A assumes a specific value and the solution is termed the PARTICULAR SOLUTIO . When we use the GC to plot out a series of graphs for various values ofA, the result is that we produce a family of solution curves.
a (2) 2 −2b=0⇒b=2a ∴ =ax2 −2ax=ax(x− 2) dt dx (shown) Example: A rectangular tank has a horizontal base. Water is flowing into the tank at a constant rate, and flows out at a …
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