Question

The general solution of a differential equation of the type  `dx/dy + P_1 x = Q_1` is ______.

Options

• `y e^(intP_1 dy) = int(Q_1 e^(intP_1 dy)) dy + C`

• `y . e^(intP_1 dx) = int(Q_1 e^(intP_1 dx)) dx + C`

• `x e^(intP_1 dy) = int(Q_1 e^(intP_1 dy)) dy + C`

• `xe^(intP_1 dx) = int(Q_1 e^(intP_1 dx)) dx + C`

Answer 1

The general solution of a differential equation of the type  `dx/dy + P_1 x = Q_1` is `underline(x  e^(int P_1 dy) = int (Q_1e^(int P_1dy)) dy + C)`.

Explanation:

Given the differential equation

`dx/dy + P_1 x = Q_1`

where P₁ and Q₁ are functions of y.

∴` I.F. = e^(int P_1dy)`

Hence, the required solution

`x * e^(P_1dy) = int (Q_1 xx e^(int P_1 dy))dy + C`