# How to solve this y'= 2 + (1+sint)y/5

1. Jun 25, 2014

### kochibacha

it's linear ordinary differential equation and when i tried to solve the integrating factor cannot be put in an elementary form. The text i that i got this equation tell me to plot y versus t for several constant C so there must be the exact solution

2. Jun 25, 2014

3. Jul 1, 2014

### HallsofIvy

The point of an integrating factor, $\alpha$, is that it allows us the write the parts including y as a single derivative: $(\alpha y)'= \alpha y'+ \alpha' y$ and here we want that to equal $y'- (1+ sin(t))y$. That is, we want $\alpha'= d\alpha/dt= -1 - sin(t)$ which is "separable".

4. Jul 2, 2014

### HallsofIvy

I should have said
$$\frac{d\alpha}{dt}= (-1- sin(t))\alpha$$

5. Jul 2, 2014

### Simon Bridge

@kochibacha: any of this useful?