logistic_guy
Senior Member
- Joined
- Apr 17, 2024
- Messages
- 2,214
Solve.
\(\displaystyle (y^2 + 1) \ dx = y \sec^2 x \ dy\)
\(\displaystyle (y^2 + 1) \ dx = y \sec^2 x \ dy\)
kids' differential equation
- Thread starter logistic_guy
- Start date
logistic_guy
Senior Member
- Joined
- Apr 17, 2024
- Messages
- 2,214
\(\displaystyle (y^2 + 1) \ dx = y \sec^2 x \ dy\)
\(\displaystyle \frac{1}{\sec^2 x} \ dx = \frac{y}{y^2 + 1} \ dy\)
\(\displaystyle \cos^2 x \ dx = \frac{y}{y^2 + 1} \ dy\)
\(\displaystyle \int \cos^2 x \ dx = \int \frac{y}{y^2 + 1} \ dy\)
\(\displaystyle \frac{1}{2}\int (1 + \cos 2x) \ dx = \frac{1}{2}\int \frac{2y}{y^2 + 1} \ dy\)
\(\displaystyle \textcolor{blue}{\frac{x}{2} + \frac{\sin 2x}{4} = \frac{1}{2}\ln\left(y^2 + 1\right) + c}\)