Question

(D³+4D²D¹+4DD¹^2)Z=0

Answer 1

Since,highest power of Di.e., 3 is greater than highest power ofD^'i.e., 2.

Therefore, put D=m and D'=1.

Then, the Auxiliary equation is,

m³+4m²+4m=0

m(m²+4m+4)=0

m(m+2)²=0

m=-2,-2,0

Therefore, the complementary function ia given by,

C.F= $\phi(y-2x)+x\phi(y-2x)+\phi(y)$