A solution to an initial value problem y fx y y y 2 4 y 2

A solution to an initial value problem y’’ = f(x, y, y ‘), y (2) = 4, y ‘(2) = 5 is

A. a curve that passes the point (2, 2) and has a slope of 4.

B. a curve that passes the point (2, 4) and has a slope of 4.

C. a curve that passes the point (2, 5) and has a slope of 5.

D. a curve that passes the point (2, 4) and has a slope of 5.

Here y(2)=4 is written in form y=f(x)

so clearly when x =2 then y=4

that means a point in form (x,y) on original graph will be (2,4) or it will pass from point (2,4).

Further as slope is actually the derivation of the function at a given point,

so slope of function y=f(x) is represented as slope = dy/dx = y`

so y`(2)=5 means that at x=2, y`=5 or at x=2, it slope is 5.

So based on these two conclusions, correct answer is :

OPTION D.

Answer