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

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

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