1. Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.)

y² = 3kx³

2. Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.)

x² + 2y² = 13k²

3. Solve the initial-value problem

y' = (6 sin(x))/sin(y), y(0) = /2.

4. Solve the differential equation.

du

dt

=

1 + t⁴

ut² + u⁴t²

5. Solve the differential equation.

dz

dt

+ 7e^{t + z} = 0