The general solution of y" - m2y = 0 isa)cj sinh mx + c2 cosh mxb)c1 cos mx + c2 sin mxc)c1cos mx + c2 sinh mxd)c1 sin mx + c2 cosh mxCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Correct Answer :- A

Explanation : y''- m²y = 0

r² - m² = 0

r = +-m

y = Ae^mx + Be^-mx

Let A=C+D and B=D-C

= Ce^mx + De^mx - Ce^-mx + De^-mx

= C(e^mx-e^-mx) + D(e^mx+e^-mx)

= Csinh(mx) + Dcosh(mx)

Answer

The general solution of a problem refers to a set of solutions that satisfy all possible conditions or constraints of the problem. It is a solution that encompasses all possible specific solutions.

In mathematics, the general solution of a differential equation is a solution that includes all possible solutions of the equation. It typically involves constants or arbitrary functions that can take any value.

In physics, the general solution of an equation of motion or a wave equation represents all possible solutions that satisfy the given initial conditions and boundary conditions.

In computer science, the general solution of a problem refers to an algorithm or a method that can be applied to solve the problem for any given input.

Overall, the general solution provides a comprehensive and inclusive approach to solving a problem by considering all possible solutions.

Answer

Y''-m^2y=0
r^2-m^2=0 characteristic

r=+-m

y=Ae^mx+Be^-mx
=Ce^mx+De^mx-Ce^-mx+De^-mx(Let A=C+D and B=D-C)
=C(e^mx-e^-mx)+D(e^mx+e^-mx)
=Csinh(mx)+Dcosh(mx)

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