Question

P 6. (6 pts) Mark each statement as True or False.

A. “Suppose that y_p is a particular solution of the ODE a₂(x)y′′ + a₁(x)y′ + a₀(x)y =g(x). Then 3y_p is another particular solution of the ODE.”

B. “Suppose that y₁ is a solution of the ODE a₂ (x)y′′ +a₁(x)y′ +a₀(x)y= 0. Then 3y₁ is another solution of the ODE.”

Answer 1

First statement is false because the give question is non homogeneous if we uses the 3y1 as a particular solution that will lead to a multiple factor of 3 in LHS which won't be equal to g(x ) in RHS as it was for y1.

2nd statement is true because that 3y1 factor will go under zero in RHS. As it is a homogeneous equation the constant factor multiple won't change the solution it independent of constant factor even 5 y1 would be a solution for this ODE.

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