Prove that is the general solution of differential equation, where c is a parameter.

Open in App

Solution

This is a homogeneous equation. To simplify it, we need to make the substitution as:

Substituting the values of y and in equation (1), we get:

Integrating both sides, we get:

Substituting the values of I₁ and I₂ in equation (3), we get:

Therefore, equation (2) becomes:

Hence, the given result is proved.

Suggest Corrections

Similar questions

Q. Prove that is the general solution of differential equation , where c is a parameter.

Prove that $x^{2} - y^{2} = C (x^{2} + y^{2})^{2}$ is the general solution of differential equation $(x^{3} - 3 x y^{2}) d x = (y^{3} - 3 x^{2} y) d y,$ where C is a parameter.

Q. Show that the general solution of the differential equation is given by ( x + y + 1) = A (1 – x – y – 2 xy ), where A is parameter

Show that the general solution of the differential equation $\frac{d y}{d x} + \frac{y^{2} + y + 1}{x^{2} + x + 1} = 0$ is given by $(x + y + 1) = A (1 - x - y - 2 x y)$ , where A is a parameter.

Show that the general solution of the differential equation is given by (x + y + 1) = A (1 – x – y – 2xy), where A is parameter

Join BYJU'S Learning Program