of differential equation Question 1. Solve the differential equation: $\frac{dy}{dx} = 2x + y + 1$.
Solution:
$\int \frac{dy}{dx} dx = \int (2x + y + 1) dx$
$y = x^2 + xy + x + C$
Question 2. Solve the differential equation: $\frac{dy}{dx} = 3x^2 + 2x$.
Solution:
$\int \frac{dy}{dx} dx = \int (3x^2 + 2x) dx$
$y = \frac{3x^3}{3} + x^2 + C$
Question 3. Solve the differential equation: $\frac{dy}{dx} = x^2 + 2xy + 2y^2$.
Solution:
$\int \frac{dy}{dx} dx = \int (x^2 + 2xy + 2y^2) dx$
$y = \frac{x^3}{3} + xy^2 + y^
