Question

3x²d²y/dx²-x²dy/dx-2y=0

Answer 1

Answer:

Let us see if the equation:

D2+D−2=0D2+D−2=0

has real solutions:

D2+2D2+14−14−2=0⇒D2+2D2+14−14−2=0⇒

⇒(D+12)2−214=0⇒⇒(D+12)2−214=0⇒

⇒(D+12)2−(112)2=0⇒⇒(D+12)2−(112)2=0⇒

⇒(D−1)(D+2)=0⇒(D−1)(D+2)=0

So, you can use now the roots to find the general solution:

y=Aex+Be−2xy=Aex+Be−2x

It works because if you substitute:

y=eDxy=eDx

then:

y′=DeDxy′=DeDx

and

y′′=D2eDxy″=D2eDx

So,

y′′+y′−2y=(D2+D−2)eDxy″+y′−2y=(D2+D−2)eDx

537 viewsAnswer requested by 

PLEASE MARK ME AS BRAINLIEST