Question

For the differential equation $\frac{d^{2}y}{d{x}^2}+y=0$, if there is a function $y=\varphi (x)$ that will satisfy it, then the function $y=\varphi (x)$ is called

• A. solution curve only
• B. integral curve only
• C. solution curve or integral curve
• D. None of the above

Answer 1

Answer: (C)

Consider the differential equation $\frac{d^{2}y}{d{x}^2}+y=0$
The solution of this differential equation is a function $\varphi$ that will satisfy it i.e., when the function $\varphi$ is substituted for the unknown $y$ (dependent variable)in the given differential equation, LHS becomes equal to RHS.
The curve $y=\varphi (x)$ is called the solution curve (integral curve) of the given differential equation