Find the general form of fx if f Solution Solve d2 fx dx2

Solution

Solve ( d^2 f(x))/( dx^2) = 5 x+4 sin(x): Integrate both sides with respect to x: ( df(x))/( dx) = integral (5 x+4 sin(x)) dx = (5 x^2)/2-4 cos(x)+c1, where c1 is an arbitrary constant. Integrate both sides with respect to x: f(x) = integral ((5 x^2)/2-4 cos(x)+c_1) dx = (5 x^3)/6-4 sin(x)+c1 x+c2, where c2 is an arbitrary constant.