How do you integrate dy/dx=(1+2x)*sqrt(y)?
We'll solve this separable differential equation in this way:
- first, we'll divide both sides by `sqrt(y)`
dy/dx*`sqrt(y)` = 1 + 2x
- now, we'll multiply both sides by dx:
dy/`sqrt(y)` = (1+2x)dx
- we'll integrate both sides:
`int` dy/`sqrt(y)` = `int` (1+2x)dx
2`sqrt(y)` = `int` dx + `int` 2x dx
2`sqrt(y)` = x + 2x^2/2 + C
`sqrt(y)` = x/2 + x^2/2 + C/2
We'll raise to square both sides to remove the square root from the left side:
y = (x + x^2 + C)^2/4
The requested primitive function is y = (x + x^2 + C)^2/4.