Consider the equation: x2 y''-6y=0 A. Could you solve this ODE using Homogeneous Linear Equations with...

Consider the equation: x² y''-6y=0

A. Could you solve this ODE using Homogeneous Linear Equations with Constant Coefficients? Explain.

B. Note that y₁=x^₃ is a solution of the ODE. Using reduction of order, find a solution y₂ such that { y₁, y₂} is linearly independent.

C. Prove that{y₁, y₂} is linearly independent.

D.What is the general solution?

Expert Solution

milcah answered 1 year ago

solve this equation y''-6y'+8y=1 when y(0)=1, y'(0)=7

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