It is called characteristic polynomial since we can find the fundamental solution set and the characteristic function in many methods like method of undetermined coefficients in elementary differential equations
Sol.[A] The parametric form of the given equation is x = t, y = t2. The equation of any tangent at t is 2xt = y t2. Differentiating, we get 2t = y1. Putting this value in the equation of tangent, we have 2 x y1/2 = y (y1/2)2 Þ 4xy1 = 4y y12
Exact Equations. A first‐order differential equation is one containing a first—but no higher—derivative of the unknown function. ... First, bring the dx term over to the left‐hand side to write the equation in standard form: Therefore, M( x,y) = y + cos y – cos x, and N ( x, y) = x – x sin y.
A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.