Is the Equation $x ^ { 2 } - y ^ { 2 } = C$

question 33

Short Answer

Is the equation $x ^ { 2 } - y ^ { 2 } = C$ , for C a constant, a solution to the differential equation $\frac { d y } { d x } = - \frac { x } { y }$ ?

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Definitions:

Justification

Providing sufficient reasons, evidence, or arguments to support a claim, belief, or action as valid or acceptable.

Premise

An assertion or proposition which forms the basis for a work's conclusion; in logic, it is the antecedent of an argument.

Simp

A slang term often used to describe someone who performs excessive subservience or attention to another person, typically someone they're interested in, often disregarding their own needs or dignity.

MP

Short for Modus Ponens, a form of argument in logic where if the first statement is true, then the second statement must also be true (If P, then Q. P, therefore Q).