Posted by **Mina** on Wednesday, May 14, 2008 at 2:15pm.

Solve the first-order initial value problem using half angle formulas

{y'(x)= 1 + sin^2 x

y (0)= -7

- Calculus -
**Reiny**, Wednesday, May 14, 2008 at 3:04pm
use the identity

cos 2x = 1 - 2sin^2 x

and solving for sin^2 x

sin^2 x = 1/2 - (1/2)cos 2x

then y'(x)= 1 + sin^2 x

becomes

y'(x)= 1 + sin^2 x

becomes

y'(x)= 1 + 1/2 - (1/2)cos 2x

= 3/2 - (1/2)cos 2x

this is now easy to integrate

Don't forget to add the constant.

plug in the point (0,-7) to find that constant.

## Answer this Question

## Related Questions

- MATH - 1.)Find the exact solution algebriacally, if possible: (PLEASE SHOW ALL ...
- Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...
- Math/Calculus - Solve the initial-value problem. Am I using the wrong value for ...
- Math Help - Hi! Can someone help check this for me and see if I'm doing it right...
- Calculus - Second Order Differential Equations - Posted by COFFEE on Monday, ...
- Chemistry - I know how to find half-lives, but I have trouble finding the length...
- Calculus - solve second-order initial value problem y"(x)= x e^-2x y'(0)= 0 y(0...
- physics - Calculate the maximum height using the initial speed, half-time, and ...
- Calculus - Second Order Differential Equations - Solve the initial-value problem...
- trig - I asked below but I guess it was not understood what I was asking. I'll ...

More Related Questions