How can i solve this problem y' = 2(3x+y)^{2}-1 when x = 0, y =0. Can someone show me the solution ?

# Differential Equation: y' = 2(3x + y)^2 - 1

## New forum topics

- I need guidance in designing a beam supporting specified ultimate moment of 1100 kN.m (doubly reinforced beam)
- I need guidance in solving the ultimate moment capacity (doubly reinforced beam)
- I need guidance in solving the balance steel area
- Please help me solve this problem using WSD (Working Stress Design) Method
- Physics: Uniform Motion
- Rescue at Sea
- Using two pumps
- Emptying a Tank
- Speed of a Plane
- Range of an Airplane

$y' = 2(3x + y)^2 - 1$

z = 3x + y

dz = 3dx + dy

dz/dx = 3 + y'

y' = dz/dx - 3

$\dfrac{dz}{dx} - 3 = 2z^2 - 1$

$\dfrac{dz}{dx} = 2z^2 + 2$

$\dfrac{dz}{dx} = 2(z^2 + 1)$

$\dfrac{dz}{z^2 + 1} = 2\,dx$

$\arctan z = 2x + c$

$\arctan (3x + y) = 2x + c$

You can now apply the initial condition to solve for the constant of integration c.