DIFFERENTIAL EQUATION

Question 1

formula for exact DE, how to solve …

Answer 1

1. identify M and N: M(x,y)dx + N(x,y)dy = 0
2. should be : ∂M/∂y = ∂N/∂x
3. F(x,y)= ∫ M(x,y)dx + ∫ M(x,y)dy + C
4. like terms should be counted as one

Question 2

formula for linear differential equation

Answer 2

ye^( ∫P(x)dx ) = ∫ Q(x) e^( ∫P(x)dx ) dx
&
xe^( ∫P(y)dy ) = ∫ Q(y) e^( ∫P(y)dy ) dy

Question 3

PROPERTIES IN A GENERAL LINEAR DIFF. EQ

Answer 3

• THE FUNCTION OF Y AND ITS DERIVATIVES OCCUR IN THE EQ IS UP TO THE 1ST DEGREE ONLY
• THE PRODUCT OF Y AND/OR ANY ITS DERIVATIVES ARE PRESENT
• NO TRANCEDENTAL FUNCTIONS OF Y OR ANY ITS DERIVATIVES OCCUR

Question 4

BERNOULI EQ.

GENERAL EQUATION, INCLUDING LINEAR DIFF EQ.

Answer 4

y^(1-n) e^([1-n] ∫P(x)dx ) = [1-n] ∫ Q(x) e^( [1-n] ∫P(x)dx ) dx

Question 5

SOLVING EQUATIONS TO FIND UNKNOWN FUNCTIONS.

Answer 5

DIFFERENTIAL EQ…

Question 6

FORMULA FOR POPULATION GROWTH

Answer 6

P(t) = P_0 e^kt

Question 7

NEWTONS LAW OF COOLING

Answer 7

T(t) = Ta + (To - Ta )e^kt

T(t) = temperature being measure
Ta = ambient temperature
k = proportionality constant
t= time

Question 8

SOLVING A DE MIXING PROBLEM

Answer 8

dQ / dt = Rin Cin - Rout [ Q/(Vo + (Rin - Rout) t) ]

Rin/out- solution rate in and rate out
Q= amount of solute and any time t
Cin/out= concentration of solute in/out
dQ/dt = rate of change of solute