# Evaluate D 4 Y D X 4 + 2 D 2 Y D X 2 + Y = 0 - Applied Mathematics 2

Sum

Evaluate (d^4y)/(dx^4)+2(d^2y)/(dx^2)+y=0

#### Solution

put d/dx=D

therefore D^4y+2D^2y+y=0

therefore D^4+2D^2+1=0

Put D^2=t

=> t^2+2t+1=0

=> t=-1, -1

Roots are : D=+i,-i,+i,-i
The complementary solution of given eqn is

y_c=y_g=(C_1+xC_2)cosx+(C_3+xC_4)sinx

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
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