ODE Maritime Flashcards
dP / dx = k - a(P + x)
Linear
dC. .
— + aC = b + kx
dx. .
Linear
` ` ` ` ` ` ` dy ‘
xy (1 + x^2) ( — ) - y^2 = 1
. . . . . . . . . . . . dx ‘
Separable
(2xy + 3y^2) (dx) - (x^2 + 2xy) (dy) = 0
Homo
` ` ` ` dy ` ` ` ` ` ` ` ` ` `
sin x ( — ) + y cos x = tan x
dx…………………
Linear
` ` ` ` ` dy `
3(x^2)(y) + (x^3)( — ) = cos x
…………..dx
Linear
dy ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
— = [ (y /x) + 6x ] / [ 2 - ln x ]
dx………………….
Exact / Linear
1 ` `` ` 1 ` ` (ax + 1) ` ` dy
—— + —— + ———— x ( — ) = 0
.x^2……y^2……….y^3…………dx
Exact
` ` dy ` ` ` ` ` ` ` `
— = e^( x - y )
dx…………………
Separable
dy ` ` ( x - y )
— = ————
dx ……. ( x + y )
Homo
y^2 ` ` ` ` ` ` ` ` ` `
—— dx + ( x - y ) dy = 0
x…………………………….
Homo
( x^2 + y^2 ) dx - 2( xy ) dy = 0
Homo
[ xe^(y / x) + y ] dx = x dy
Homo
1 ` ` ` ` e^( y^2 ) ` ` ` ` ` ` ` `
— dx + ———— dy = 0
xy ……… x^3 - 1……………….
Separable
dy ` ` ` ` ` ` ` `
— = sin^2 ( x - y )
dx……………………….
Separable
( x^2 + y^2 ) dx + 2 xy dy = 0
Homo
dy ` ` ` `
— + y = e^x
dx ……………
Linear
dy ` ` ` `
x — - 3y = x^2
dx………………
Linear
dy ` ` ` ` ` ` ` `
— = 0.05y - 3000
dt ………………………
Linear
( 5y + e^x + e^y ) dx + ( 5x + xe^y) dy = 0
Exact
( y +3 ) dx + ( cot x ) dy = 0
Separable
( x^2 + y^2 ) dx + ( 2xy + cos y ) dy = 0
Exact
( 2x + y^3 ) dx + [ 3xy^2 - e^(-2y) ] dy = 0
Exact
