CREATING DIFFERENTIAL EQUATION WORKSHEET

Form a differential equations by eliminating arbitrary constants given in brackets against each.

(i)  y²  =  4ax       {a}          Solution

(ii)  y  =  ax²+bx+c       {a, b}            Solution

(iii) x y  =  c²       {c}          Solution

(iv) (x²/a²) + (y²/b² )  =  1     {a , b}           Solution

(v) y  =  A e^2x + Be^-5x   {A , B}         Solution

(vi) y  =  (A + Bx) e^3x        {A , B}    Solution

(vii) y  =  e^3x {C cos 2 x + D sin 2 x}    {C , D}       Solution

(viii) y  =  e^mx         {m}      Solution

(ix) y = Ae^2x cos (3 x + B)      {A, B}           Solution

Find the order and degree of the following differential equations.

(1)  (dy/dx) + y  =  x²         Solution

(2)  y' + y²  =  x            Solution

(3)  y'' + 3 (y')² + y³               Solution

(4)  d²y/dx² + x  =  √[y + (dy/dx)]             Solution

(5)  d²y/dx² - y + (dy/dx + d³y/dx³)^(3/2)  =  0       Solution

(6)  y''  =  (y - (y')³)^(2/3)                   Solution

(7)  y' + (y'')²  =  (x + y'')²                  Solution

(8)  (dy/dx)² + x = (dx/dy) + x²                   Solution

Find the the following for the given differential equations.

(i) Order 

(ii) Degree

(iii) General solution

Problem 1 :

y' = 1 + x² + y + x²y

Solution

Problem 2 :

y' = x/(y² + 1)

Solution

Problem 3 :

The order and degree of the differential equation

d²y/dx² + (dy/dx)^1/3 + x^1/4 = 0

a) 2, 3    b) 3, 3    c) 2, 6     d)  2, 4

Solution

Problem 4 :

The differential equation representing the family of curves y = A cos (x + B), where A and B are parameters, is

a)  d²y/dx² - y = 0     b)  d²y/dx² + y = 0

c)  d²y/dx² = 0     d)  d²y/dx²  = 0

Solution

Problem 5 :

The order and degree of the differential equation 

√sin x (dx + dy) = √cos x (dx - dy) is

a)  1, 2      b)  2, 2     c)  1, 1     d)  2, 1

Solution

Problem 6 :

The order of the differential equation of all circles with center at (h, k) and radius a is 

a)  2    b)  3     c)  4    d)  1

Solution

Problem 7 :

The differential equation of the family of curves 

y = Ae^x + Be^-x 

where A and B are arbitrary constants is 

a)  d²y/dx² + y = 0     b)  d²y/dx² - y = 0

c)  dy/dx + y = 0     d)  dy/dx - y = 0

Solution

Problem 8 :

The solution of the differential equation 

2x (dy/dx) - y = 3

represents

a) straight lines   b) circles     c) parabola   d) ellipse

Solution

Problem 1 :

Radioactive radium has a half-life of approximately 1599 years.

A. If 50 milligrams of pure radium is present initially, when will the amount remaining be 20 milligrams? Give your answer to the nearest year.

B. What percent of a given amount remains after 100 years?

Solution

Problem 2 :

Water is leaking out of a large barrel such that the rate of the change in the water level is proportional to the square root of the depth of the water at that time. If the water level starts at 36 inches and drops to 34 inches in 1 hour, how long will it take for all of the water to drain out of the barrel?

Solution

Related pages

• Practice questions of order and degree
  
• Substitution method
• Decomposition method
• Properties of integrals
• Integration-by parts
• Integration-of Sec³ x
• Standard integrals
• Integrating quadratic denominator
• Integration-using partial fractions
• Definite integrals

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.