What can we conclude for the following linear homogeneous equation? t2y''+3ty'+y=0, t>0. y1=t is a solution. By the method of reduction of order, we can ALWAYS find another independent solution y2 satisfying W(y1,y2)≠ 0 y1=t−1 is a solution. By the method of reduction of order, we can ALWAYS find another independent solution y2 satisfying W(y1,y2)≠ 0 None of these y1=t is a solution. By the method of reduction of order, we can SOMETIMES find another independent solution y2 satisfying W(y1,y2)≠ 0 y1=t−1 is a solution. By the method of reduction of order, we can SOMETIMES find another independent solution y2 satisfying W(y1,y2)≠ 0

Required conclusion is that if  satisfies given differential equation and wronskean is zero then they are considered as solution of that differential equation.

Step-by-step explanation:

Given differential equation,

(i) To verify is a solution or not we have to show,

But,

hence is not a solution of (1).

Now if is another solution where then,

But,

so is not a solution of (1).

(ii) Rather the wronskean,

Hence it is conclude that if satisfies (i) along with condition (ii) that is wronskean zero, only then   will consider as solution of (1).

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step-by-step explanation:

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