Show that y = ax 3 + bx 2 + c is a solution of the differential equation The image displays the third-order ordinary differential equation d^3y/dx^3 = 6a.

Q10 of 462 Page 22

Show that y = ax³ + bx² + c is a solution of the differential equation

The differential equation is and the function to be proven as the solution is

y = ax³ + bx² + c; now we need to find the value of .

Putting the value of variables in the equation,

6a = 6a

As, L.H.S = R.H.S. the equation is satisfied, hence this function is the solution of the differential equation.

Verify that y² = 4ax is a solution of the differential equation

Show that Ax² + By² =1 is a solution of the differential equation

Show that is a solution of the differential equation= 0.

Show that y = e^x (A cosx + B sinx) is a solution of the differential equation