Question: 6. Given that y 1 ( x )= x^ 3 e^x is a solution of xy'' 2( x +1) y' +( x +2) y =0.

6. Given thaty1(x)=x^3e^xis a solution ofxy''2(x+1)y'+(x+2)y=0.

Hint:(fgh)'=f'gh+fg'h+fgh

'Find a second solutiony2(x) using

a) Long way of reduction of order

b) The reduction of order shortcut formula

c) Write the general solution.

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