Resolve the equation manually : dy/dx = (x ^(2))/y from x= 0 until x =0.7, with the initial condition y(0)=2. a)-using the euler explicit method (h=0.7) b)-using the euler modified method (h=0.7) c)-runge-kutta of fouth order (h=0.7) d)-calculate the error in a, b, and c.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.