(1 point) Solve the initial value problem 2yy' + 3 = y2 + 3m with y(0) = 8. a. To solve this, we should use the substitution at 2 help (formulas) With this substitution, y 2 help (formulas) y' = help(formulas) Enter derivatives using prime notation (e.g., you would enter 3;\" for g). b. After the substitution from the previous pan, we obtain the following linear differential equation in 22,1132}: '. help (equations) 0. The solution to the original initial value problem is described by the following equation in x, y. help (equations) (1 point) Solve the initial value problem 3,: ' = (x l y 4)2 with y(0) = 0. a. To solve this, we should use the substitution at 2 help (formulas) u ' = help (formulas) d Enter derivatives using prime notation (e.g., you would enter y\" for dz). b. After the substitution from the previous part, we obtain the following differential equation in :13, u, u '. help (equations) c. The solution to the original initial value problem is described by the following equation in x, y. help (equations) (1 point) Sometimes a change of variable can be used to convert a differential equation 3; ' 2 t, 3;) into a separable equation. One common change of variable technique is as follows. 1. Consider a differential equation of the form 3; ' 2 at -l y + at), where a, ,8, and 1: are constants. Use the change of variable 2 2 out + 53; + 1 to rewrite the differential equation as a separable equation of the form 2 ' = 9(2). Solve the initial value problem \"9': (HyJZL yl3)=4. (a) 9(2) = help (formulas) (b33105) = help (formulas)