Differential Equation

Question

Find the particular solution to the differential equation

d²y/dx² = -3/x⁴

given that y = 1/2

and dy/dx = −1

when x = 1.

Answer 1

y"(x)=-3x^(-4) ⇒ y'(x)=x^(-3) + k, where k is a real number

Then since y'(1) = -1 then k = -2

That is y'(x) = x^(-3) -2

Then y(x)=