Problem 2. Consider the equation: x?y"(x)- xy' +y = 0. Given that yı(x) = x is a solution of this equation. Use the method of reduction of order, find the second solution y2(x) of the equation so that and Y2 are linearly independent. (Hint: y2(x) should be given in the form y2(x) = u(x)y1(x). Y1 Substitute it into the equation to find u(x).)

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A: x+2y-z=0            i2x+3y-2y=3        ii-x-4y+3z=-2    iiii+iii-2y+2z=-2⇒-y+z=-1…

Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

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Q: Solve (1) 5-3x 2. (2) 4. 2 3 y-31 y-5 2 5 (3) 2. 4 4)

A: since we answer only first three sub-parts so we will answer first three. Please resubmit the…