The differential equation whose general solution is y^2+x=1+my where m is an arbitrary constant,

step 1 In this question we have to find the differential equation and for this differential equation we

The differential equation whose general solution is...

The differential equation whose general solution is $\mathrm{y}^{2}+\mathrm{x}=1+\mathrm{my}$ where $\mathrm{m}$ is an arbitrary constant, is (a) $\mathrm{y}=\mathrm{x} \frac{\mathrm{d} \mathrm{y}}{\mathrm{d} \mathrm{x}}+2$ (b) $\frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y=0$ (c) $x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y=0$ (d) $y=\left(x-y^{2}-1\right) \frac{d y}{d x}$

The differential equation whose general solution is $\mathrm{y}^{2}+\mathrm{x}=1+\mathrm{my}$ where $\mathrm{m}$ is an arbitrary constant, is
(a) $\mathrm{y}=\mathrm{x} \frac{\mathrm{d} \mathrm{y}}{\mathrm{d} \mathrm{x}}+2$
(b) $\frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y=0$
(c) $x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y=0$
(d) $y=\left(x-y^{2}-1\right) \frac{d y}{d x}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

General Solution

A general solution to a differential equation represents a family of curves that includes an arbitrary constant. This constant accounts for the various specific solutions that satisfy the differential equation under different initial conditions.

Arbitrary Constant

The arbitrary constant in a general solution reflects the inherent degree of freedom in the family of solutions of a differential equation. Its presence shows that there are multiple curves or functions that satisfy the differential equation.

Elimination of Arbitrary Constants

Deriving the differential equation from a given general solution often requires eliminating the arbitrary constant. This is typically done by differentiating the general solution with respect to the independent variable and then algebraically removing the constant.

Implicit Differentiation

When a general solution is presented in an implicit form (i.e., as a relation involving both the dependent and independent variables), implicit differentiation is used to differentiate the equation with respect to the independent variable, allowing for the elimination of the arbitrary constant.

Transcript

Please give Ace some feedback