Verify that the indicated function y=ϕ(x)y=ϕ(x) is an explicit solution of the given first-order differential
equation. By considering ϕϕ simply as a function, give its domain. Then by considering ϕϕ as a
solution of the differential equation, give at least one interval II of definition.
y′=25+y2;y=5tan5xy ′ =25+y 2 ;y=5tan5x

Precipitation hardening can be achieved in many light alloys by a three-step heat treatment. what is carried out and what is the purpose at each step? why is such a treatment necessary based on the nucleation and growth theory of phase transformation. compare this treatment with tempering martensite for carbon steels (similarities and differences).