5. Find the general solution for 2 x + y2 + 2 xyy' = 0 6. Find the integrating factor for the following equation and then solve it, (a + 2)sing + (xcosy)y' = 0, y(1) = 7. Solve 1+ (- - siny)y' = 0 y4. A secondorder chemical reaction involves the interaction of one molecule of a substance P with one molecule of a substance Q to produce one molecule of a new substance X; this is denoted by P + (,2 > X. Suppose that p and q, where p 75 q, are the initial concentrations of P and Q, respectively, and let 11(t) be the concentration of X at time t. Then p 33(t) and q 3305) are the concentrations of P and Q at time t, and the rate at which the reaction occurs is given by the equation d, df = ate mm as): where oz is a positive constant. (a) if 93(0) : 07 determine the limiting value of 1(t) as t > 00 without solving the differential equation. Then solve the initial value problem and nd 3:05) for any t. (b) If the substances P and Q are the same, then p 2 q and the equation is replaced by (is: dt : 01(39 mlz- If 22(0) : 0, determine the limiting value of 22(t) as t > 00 without solving the differential equation. Then solve the initial value problem and determine 33(t) for any t