Differential Equations by Separation of Variables - Classwork
dy
! f ( x ) ! g( y ) . In order to solve it, you must put it in the form of
dx
g( y ) ! dy ! f ( x ) ! dx allowing you to integrate. Your goal is to get an equation in the form of y ! h ( x )
dy 2 x
dy
dy x $ sin( x )
1)
3)
!
2)
! y2
!
3y 2
dx
y
dx
dx
A differential equation will be in the form of
4)
dy
! 4y
dx
7.
du
! e u $2 t
dt
5.
dy
! ky
dx
6)
8.
dy
! xy
dx
dx
! 1 $ t " x " tx
dt
Find the solution of the differential equation that satisfies the given condition.
dx
dy 1 $ x
! 1 , x (0) ! 1
10.
, y (1) ! "4
9. xe" t
!
dt
dx
xy
11.
dy
! y 2 $ 1 , y (1) ! 0
dx
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12. x $ 2 y x 2 $ 1
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dy
! 0 , y (0) ! 1
dx
Stu Schwartz
Differential Equations by Separation of Variables - Homework
1.
dy x
!
dx y
3. x
dy
!y
dx
2.
dy x 2 $ 2
!
dx
3y 2
4.
(2 $ x )
dy
! 3y
dx
6. (1 $ 4 x 2 ) y # ! 1
5. yy # ! sin x
Find the solution of the differential equation that satisfies the given condition.
dy
dy
! 0 , y (1) ! 4
8. y
! e x , y (0) ! 4
7. x $ y
dx
dx
9. xy
dy
" ln x ! 0 , y (1) ! 0
dx
11. (1 $ x 2 )
10. y ( x $ 1) $
dy
" (1 + y 2 ) ! 0 , y (0) ! 3
dx
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dy
! 0 , y ("2) ! 1
dx
12. dT $ k (T " 70) dt ! 0 , T (0) ! 140
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Stu Schwartz