Find the general solution of the given higher-order differential equation. y^{(4)}+y'''+y''=0 y(x)=

Mary Reyes

Mary Reyes

Answered question

2021-12-12

Find the general solution of the given higher-order differential equation.
y(4)+y+y=0
y(x)=

Answer & Explanation

abonirali59

abonirali59

Beginner2021-12-13Added 35 answers

The characteristic equation is r4+r3+r2=0 
r4+r3+r2=0 
r2(r2+r+1)=0 
Observe that r=0 is a root with multiplicity 2.
r=1±124(1)(1)2(1) 
r=1±124(1)(1)2(1)  =1±i32 
The answer y(x)=c1+c2x+c3ex2cos(32x)+c4ex2sin(32x)

Orlando Paz

Orlando Paz

Beginner2021-12-14Added 42 answers

Thank you, you helped me a lot!

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