ODE Maritime

Question 1

dP / dx = k - a(P + x)

Answer 1

Linear

Question 2

dC. .
— + aC = b + kx
dx. .

Answer 2

Linear

Question 3

` ` ` ` ` ` ` dy ‘
xy (1 + x^2) ( — ) - y^2 = 1
. . . . . . . . . . . . dx ‘

Answer 3

Separable

Question 4

(2xy + 3y^2) (dx) - (x^2 + 2xy) (dy) = 0

Answer 4

Homo

Question 5

` ` ` ` dy ` ` ` ` ` ` ` ` ` `
sin x ( — ) + y cos x = tan x
dx…………………

Answer 5

Linear

Question 6

` ` ` ` ` dy `
3(x^2)(y) + (x^3)( — ) = cos x
…………..dx

Answer 6

Linear

Question 7

dy ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
— = [ (y /x) + 6x ] / [ 2 - ln x ]
dx………………….

Answer 7

Exact / Linear

Question 8

1 ` `` ` 1 ` ` (ax + 1) ` ` dy
—— + —— + ———— x ( — ) = 0
.x^2……y^2……….y^3…………dx

Answer 8

Exact

Question 9

` ` dy ` ` ` ` ` ` ` `
— = e^( x - y )
dx…………………

Answer 9

Separable

Question 10

dy ` ` ( x - y )
— = ————
dx ……. ( x + y )

Answer 10

Homo

Question 11

y^2 ` ` ` ` ` ` ` ` ` `
—— dx + ( x - y ) dy = 0
x…………………………….

Answer 11

Homo

Question 12

( x^2 + y^2 ) dx - 2( xy ) dy = 0

Answer 12

Homo

Question 13

[ xe^(y / x) + y ] dx = x dy

Answer 13

Homo

Question 14

1 ` ` ` ` e^( y^2 ) ` ` ` ` ` ` ` `
— dx + ———— dy = 0
xy ……… x^3 - 1……………….

Answer 14

Separable

Question 15

dy ` ` ` ` ` ` ` `
— = sin^2 ( x - y )
dx……………………….

Answer 15

Separable

Question 16

( x^2 + y^2 ) dx + 2 xy dy = 0

Answer 16

Homo

Question 17

dy ` ` ` `
— + y = e^x
dx ……………

Answer 17

Linear

Question 18

dy ` ` ` `
x — - 3y = x^2
dx………………

Answer 18

Linear

Question 19

dy ` ` ` ` ` ` ` `
— = 0.05y - 3000
dt ………………………

Answer 19

Linear

Question 20

( 5y + e^x + e^y ) dx + ( 5x + xe^y) dy = 0

Answer 20

Exact

Question 21

( y +3 ) dx + ( cot x ) dy = 0

Answer 21

Separable

Question 22

( x^2 + y^2 ) dx + ( 2xy + cos y ) dy = 0

Answer 22

Exact

Question 23

( 2x + y^3 ) dx + [ 3xy^2 - e^(-2y) ] dy = 0

Answer 23

Exact