MAT136H1 Lecture Notes - Integral Curve, Differential Equation

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: all

Document Summary

Question #1 (medium): sketching the direction field for differential equation. Differential equation for a given combination of and , the slope at that coordinate is equal to which is given by the differential equation. You can keep track of these coordinates along with the slope at the point, or take some sample values for the slope and work out the equation backward for and relationship that produces that slope anywhere. Then for connect these short slope lines at a given point as a sketch representing the solution curve passing through that point. Sketch a direction field for the differential equation. Then use it to sketch three solution curves. The given differential equation is affected only by the y variable and not . First draw the and axis, and lay out the grid lines focusing on the values that affect the slope. When , , so all along the x-axis the slope will be , thus a horizontal tangent.