(-)C' @1" 5 Courses Homework Sets HW3 Problem 6 User Settings Previous Problem Problem List Next Problem Grades HW3: Problem 6 (1 point) In case an equation is in the form y' : f(aa: + by + C), Le, the RHS is a linear function of a: and y. We will use the substitution 1} = (1:1: -i- by + c to find an implicit general solution. - The right hand side of the following rst order problem Problem 1 J Problem 2 J Problem 3 is a function ofa linear combination of a: and y, Le, 11' = ax + by + c) . To solve this problem we use the substitution Problem 4 U : (1:1: + by + c which transforms the equation into a separable equation. y'=(5m6y+3)5+%, y(0)=0 Problem 5 We obtain the following separable equation in the variables a: and 11: Problem 6 Problem 7 J l" = l Problem 8 Problem 9 Problem 10 z / l = 0. Problem 11 \\ Problem 12 J Solving this equation an implicit general solution in terms of :12, 'U can be written in the form Transforming back to the variables :1: and y we obtain an implicit solution Problem 13 :1:-- l : C. Problem 14 Problem 15 Next using the initial condition y(0) = 0 we nd C = l l - Then, after a little algebra, we can write the unique explicit solution of the initial value problem as 4 l0 PM 7 OZ'l F Mostly (lotldy