Question

solve the initial value problem
dy/dx=2x^(-3/4), y(1)=1
I got y=-3/4x^(-7/4)-7/4 is that correct?

Answer 1

\[\frac{dy}{dx} = 2x^{-\frac{3}{4}}\]\[\int dy =\int 2x^{-\frac{3}{4}}dx\]\[y = 8x^{\frac{1}{4}} + C\]\[1 = 8(1)^{\frac{1}{4}} + C\]\[C = -7\]\[y = 8x^{\frac{1}{4}} - 7\]

Answer 2

wow, thanks so much!