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System of Linear Equations: Solving and Identifying Dependent Equations, Exams of Differential Equations

PJA SchoolDifferential Equations

A collection of 30 linear equations in the form of dx/dy and dy/dx. The goal is to identify dependent equations and find their solutions. Some equations are given with specific values for x and y, while others are left in general form. Useful for students studying advanced mathematics, particularly those focusing on linear algebra and calculus.

What you will learn

  • What is the general method for solving a system of linear equations?
  • Can you find the solutions for the given system of linear equations?
  • How to identify dependent equations in a system of linear equations?

Typology: Exams

2020/2021

Uploaded on 11/14/2021

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bg1
1.
(
x2−xy +y2
)
dx−xydy =0
2.
xydx +
(
x2+y2
)
dy=0
3.
(
x−2y
)
dx+
(
2x+y
)
dy=0
4.
[
xcsc
(
y
x
)
−y
]
dx +xdy=0
5.
(
x2+y2
)
dx−xydy=0
6.
xydx−
(
x2+3y2
)
dy=0
7.
(
x3+2
)
y=x
(
y4+3
)
y '
8.
9.
mydx=nxdy
10.
xcos2ydx +tanydy =0
11.
(
x+2
)
dx=
(
x+3
)
sinycosydy
12.
x2y y'=ey
13.
(
e2x+4
)
y'=y
14.
y'=ysecx
15.
xy3dx +
(
y+1
)
e−xdy =0
16.
(
3x2y−6x
)
dx +
(
x3+2y
)
dy=0
17.
(
2x3−xy2−2y+3
)
dx−
(
x2y+2x
)
dy=0
18.
[
e2y−ycos
(
xy
)
]
dx +
(
2xe2y−xcosxy +2y
)
dy=0
19.
(
y2cosx−3x2y−2x
)
dx +
(
2ysinx−x3+lny
)
dy=0
20.
[xdy
dx +y=x3]1
x
21.
dy
dx +y=e2x
22.
(
x+3y
)
dx−xdy =0
23.
ydx +
(
3x−xy +2
)
dy=0
24.
y
(
6y2−x−1
)
dx +2xdy=0
25.
2dy
dx −y
x=5x3y3
26.
dy +ydx=2xy2exdx
27.
dx−2xydy=6x3y2e−2y2
dy
28.
(y¿¿ 4−2xy )dx+3x2dy=0¿
pf2

Partial preview of the text

Download System of Linear Equations: Solving and Identifying Dependent Equations and more Exams Differential Equations in PDF only on Docsity!

1. ( x^2 − xy + y^2 ) dx − xydy = 0

2. xydx +( x^2 + y^2 ) dy = 0

  1. ( x − 2 y ) dx + ( 2 x + y ) dy = 0

[

xcsc (

y

x )

− y

]

dx + xdy = 0

5. ( x^2 + y^2 ) dx − xydy = 0

6. xydx −( x^2 + 3 y^2 ) dy = 0

7. ( x^3 + 2 ) y = x ( y^4 + 3 ) y '

8. ye^2 x^ dx =( 4 + e^2 x^ ) dy

  1. mydx = nxdy
  2. (^) xcos^2 ydx + tanydy = 0
  3. (^ x^ +^2 )^ dx =(^ x +^3 )^ sinycosydy
  4. (^) x^2 y y' = e y

13. ( e^2 x^ + 4 ) y' = y

  1. (^) y'^ = ysecx
  2. xy 3 dx + ( y + 1 ) e − x dy = 0

16. ( 3 x^2 y − 6 x ) dx +( x^3 + 2 y ) dy = 0

17. ( 2 x^3 − xy^2 − 2 y + 3 ) dx −( x^2 y + 2 x ) dy = 0

  1. (^) [ e^2 y − ycos ( (^) xy ) (^) ] dx +( (^2) xe^2 y − xcosxy + 2 y ) (^) dy = 0

19. ( y^2 cosx − 3 x^2 y − 2 x ) dx +( 2 ysinx − x^3 + lny ) dy = 0

  1. [^ x^ dy dx
    • y = x 3 ]

x

dy dx

  • y = e 2 x
  1. (^ x^ +^3 y^ )^ dx − xdy =^0
  2. ydx^ +(^3 x − xy^ +^2 )^ dy =^0

24. y ( 6 y^2 − x − 1 ) dx + 2 xdy = 0

dy dx

y x = 5 x 3 y 3

  1. (^) dy + ydx = 2 xy^2 ex^ dx
  2. (^) dx − 2 xydy = 6 x^3 y^2 e −^2 y 2 dy
  3. (^) ( y ¿¿ 4 − 2 xy ) dx + 3 x^2 dy = 0 ¿

29. ( 3 xy^3 + 4 y ) dx +( 3 x^2 y^2 + 2 x ) dy = 0

30. ( 2 xy^2 − 2 y ) dx +( 3 x^2 y − 4 x ) dy = 0

  1. (2x+3y-1)dx+(2x+3y-5)dy=
  2. (1+3xsiny)dx-x^2cosydy=
  3. dy/dx=sin(x+y)
  1. (x-2y+4)dx+(2x-y+2)dy=
  2. (2x+3y-1)dx+(2x+3y+2)dy=0 when x=1,y=
  3. (2x+3y-1)dx-4(x+1)dy=
  1. y(y^3-x)dx+x(y^3+x)dy=
  2. y(x^2+y^2-1)dx+x(x^2+y^2+1)dy=
  3. y(x^3-y)dx-x(x^3+y)dy=
  1. (3xy^3+4y)dx+(3x^2y^2+2x)dy=
  2. (2xy^2-2y)dx+(3x^2y-4x)dy=
  1. (x+2y-1)dx+3(x+2y)dy=
  2. (1+3xsiny)dx-x^2cosydy=
  1. (x+y-4)dx-(x-y+2)dy=
  2. (x-2y+3)dx+(4x+y+3)dy=
  3. (2x-5y+3)dx-(2x+4y-6)dy=
  1. (x+2y-4)dx-(2x+y-5)dy=