Question

Consider the following statements:
$1.$ The general solution of $\frac{dy}{dx}=f\left(x\right)+x$ is of the form $y=g\left(x\right)+c$, where $c$ is an arbitrary constant.
$2.$ The degree of ${\left(\frac{dy}{dx}\right)}^2=f\left(x\right)$ is $2$.
Which of the above statements is/are correct?

• A. $1$ only
• B. $2$ only
• C. Both $1$ and $2$
• D. Neither $1$ nor $2$

Answer 1

The correct option is C Both $1$ and $2$

1. As the RHS of the equation is a function of x, Integrating wrt x gives general solution of the form $y=g\left(x\right)+c$

2. The order of a differential equation is the power of the highest order derivative present in the equation.

Hence, here the degree is $2$.

Thus both the statements 1 and 2 are correct.