Use the method of reduction of order to find a second solution to t^2y' + 3ty' – 3y = 0, t> 0 given yı(t) = t y2(t) = preview give your answer in simplest form (ie no coefficients)

Let . Then

and substituting these into the ODE gives

Let , so that . Then the ODE is linear in , with

Multiply both sides by , so that the left side can be condensed as the derivative of a product:

Integrating both sides and solving for gives

Integrate again to solve for :

and finally, solve for by multiplying both sides by :

already accounts for the term in this solution, so the other independent solution is .

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b