Help me prove differential equation

[zabcima]

please help me find the answer..

1. Prove that lny=C_1e^x+ C_2e^-x is the solution of differential equation
yy''-(y')^2 =y^2lny note:(C_1)meaning C sub 1, a constant value


2. y^-3=x^3(3e^x+c) is the solution of differential equation xy'+y+x^4y^4e^x=0
note: a while ago i forgot to emphasize that the value of y'' is that it is a double prime.
pls.! help me prove it.thanks

 

[Hootenanny]

please help me find the answer..

1. Prove that lny=C_1e^x+ C_2e^-x is the solution of differential equation
yy''-(y')^2 =y^2lny note:(C_1)meaning C sub 1, a constant value


2. y^-3=x^3(3e^x+c) is the solution of differential equation xy'+y+x^4y^4e^x=0
note: a while ago i forgot to emphasize that the value of y'' is that it is a double prime.
pls.! help me prove it.thanks

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We are more than happy to help you, but you must show some effort in attempting to solve the problems yourself.

HINT: The solution of a differential equation, by definition, satisfies the differential equation.