January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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The general solution is
ð
dy
gðyÞ
5
ð
f ðxÞdx 1 C
Exact equation s: Mðx; yÞdx 1 Nðx; yÞdy 5 0 is called exact if @M=@y 5 @N=@x
and not exact otherwise.
The general solution is
ð
Mðx; yÞdx 1
ð
Nðx; yÞdy 5 C
Homogeneous equations: dy=dx 5 f ðx; y Þ is homogeneous if the function
f ðtx; tyÞ5 f ðx; yÞ
The substitution z 5 y=x converts the equation to separable
xðdz=dxÞ1 z 5 f ð1; zÞ
Bernoulli equations:
dy
dx
1 gðxÞy 5 f ðxÞy
n
The substitution z 5 y
12n
converts the equation to linear ðdz=dxÞ1
ð1 2 nÞgðxÞz 5 ð1 2 nÞf ðxÞ
5.37 Second-Order Differential Equations
Homogeneous linear equat ion with constant coefficients: y
00
1 by
0
1 cy 5 0. The
characteristic equation is λ
2
1 b
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