2. Use the method of isoclines to sketch the direction field for the differential equation y' — y² — t² = 0 and sketch some solution curves for the equation. Determine the behavior of the solutions as t±o.
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- Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.dy =x-Y. Consider the differential equation dx a) What is the slope of the direction field at the point (-1.5, -1.5) ? b) What is the slope of the direction field at the point (-0.5, 1.5) ? c) What is the slope of the direction field along the x-axis? Enter a number or an expression. d) What is the slope of the direction field along the y-axis? Enter a number or an expression. e) Use your answers above to choose the correct direction field for the differential equation. III/ 1117/ 1117/ || | // -²¹, 111/1. III/ ¹+ 111/42- IQ 1 I - 1²₁ VAI NATI NAII SI C MDraw a direction field (slope field) of y' = x. Use all 25 grid intersections. 2 1 2