Consider the equation d²u dx² P₂(x)- du dx + P₁(x). + po(x)u = 0. dx y By introducing a new function y(x) by u = exp (f dr. the Riccati equation dy Po P1 - y². dx P2 P2 show that Y satisfies The general solution of the second-order equation for u has two arbitrary constants. The general solution of the first-order equation for y has one arbitrary constant. Explain how this contradiction can be resolved.

Q: FLUENCY 1. Which of the following is a quadratic function? (1) y= 3x-2 (3) y=x -4 (2) y = x' +2x -1…

A:

Q: Differentiate the function. g'(t) = g(t) = In t(t² + 1)8 3 4t 1 -

A:

Q: Is the function f(2) = -2(xy+x)+i(x² – 2y – y) differentiable? If it is, find it's derivative.

A: Consider the given function.

Q: If f(x) = ax+b „x # - , find an equation for f~²(x). Cx+d c'

A: inverse of f(x) = ?

Q: y (3x² √ + 1 ) dx = (-) dy solve exact equation

A: Step 1: Step 2: Step 3: Step 4:

Q: Find d³y/dx³. y(x) 2STENTOR x(x-1) 3

A:

Q: Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dy…

A: To find the slope of the tangent line to the curve  at the point .

Q: Solve (1+x)dy-ydx=0

A:

Q: dž 3 9. with x(0) = dt -1 -3 x1(t) = help (formulas) x2(t) : help (formulas)

A:

Q: A linear model of the spread of an epidemic in a community of 1000 people is the equation: dx/dt =…

A: To find the number of people x(t) who have contracted the disease at the time oftime t.

Q: x2 + a Consider the function Find the value of the constant a so that y' (1) = 0.64

A:

Q: Determine for which values of m the function (x)=x" is a solution to the given equation. (a) 3,2d…

A: We have to find the value of m.

Q: 3x Write down the derivative of the function V3+ cos? (x) dxc.

A: