Differential Equations, Mathematics: XII

 1.      What is the order and degree of the differential equation whose solution is y =   cx+ c² - 3c^3/2 + 2, where c is a parameter.                                                                                     

2.      Verity that the function is a solution of the corresponding diff. eq.  x + y = tan-1  y ; y2y1   + y2   + 1 = 0

3.      Form the differential equation representing the family of ellipses having foci on x – axis and centre at the origin.

4.      Form the diff. eq of the family of circles touching the x axis at origin.                     

5.      Solve the diff eq.ex    tan y dx +  (1  - ex)Sec2 y dy = 0

ç       ÷

6.      Solve Cos æ dy ö  =a, ; y = 1 when x = 0

                          è dx ø

7.      Solve.  x 2   - y2dx+2xy dy = 0                                                                                            

 8.      Solve: x²dy + y(x + y)dx = 0 for y = 1, x = 1                                                                                     

                              

9.      Find the particulars solution of diff . Equation.(1+x 2  dy +2xy dx =Cotx dx

 10.    Find the particular solution of diff. equation

x dy     y  - x  + xy Cot x = 0

dx

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