The Marshallian demand function for good x is given by: x = I/(2p_x).The compensated demand function for good x is given by: x^c= [(p_y/p_x)U]^1/2. The indirect utility function for this consumer choice problem is given by:V(p_x, p_y, I) = I²/4p_xp_y. In this example, the substitution effect for good x own-price change (as opposed to cross-price effect) is given by the following equation:-a(I/p_x²), where a is a constant. Constant a is equal to what?

Please show steps to solve for "a".

I attempted to differentiate dx/dpx and dxc/dpx. I do not think my solution for dxc/dpx is correct, and when I substitute indirect utility function V for U, I am unsure how to simplify this to get the substitution effect formula.