Solve the initial-value problem for y as a function of x.

Question

Solve the initial-value problem for y as a function of x. (x^2+25)dy/dx=1,y(5) = 0

Answer 1

dy/dx=1/(x²+5)

The antiderivative is an arctan function and you can get it using the substitution x=5 tan θ.

Answer 2

(x²_{+25) (dy/dx) = 1}

y' = 1/((x²₊₂₅₎₎

_y=∫ (1/((x²_{+25)) dx = (1/5)arctan(x/5) + C}

_{y(5) = (1/5) arctan(1) +C = 0, (1/5)(Π/4) +c =0}

_{y=(1/5)arctan(x/5) - Π/20}