Question

Sketch orthogonal trajectories online for a given differential equation.

Answer 1

To sketch orthogonal trajectories for a given differential equation, differentiate the equation to find the slope of the original curves. Take the negative reciprocal of the slope to find the slope of the orthogonal trajectories. Integrate the slope of the orthogonal trajectories to obtain the equation of the orthogonal curves. Plot both the original curves and the orthogonal curves on the same graph to see how they intersect.

Step-by-step explanation:

To sketch orthogonal trajectories for a given differential equation, follow these steps:

1. Differentiate the given differential equation to find the slope of the original curves.
2. Take the negative reciprocal of the slope to find the slope of the orthogonal trajectories.
3. Integrate the slope of the orthogonal trajectories to obtain the equation of the orthogonal curves.
4. Plot both the original curves and the orthogonal curves on the same graph to see how they intersect.