(1 point) In case an equation is in the form y'= f(a+by+c), i.e., the RHS is a linear function of and y. We will use the

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1 Point In Case An Equation Is In The Form Y F A By C I E The Rhs Is A Linear Function Of And Y We Will Use The 1 (70.49 KiB) Viewed 74 times

(1 point) In case an equation is in the form y'= f(a+by+c), i.e., the RHS is a linear function of and y. We will use the substitution v= a +by+e to find an Implicit general solution. The right hand side of the following first order problem y = (3x − 3y + 1) 5/6 +1, y(0) = 0 Is a function of a linear combination of z and y, l.e., y' = f(az +by+c). To solve this problem we use the substitution v = a +by+c which transforms the equation into a separable equation. We obtain the following separable equation in the variables and v: d = Solving this equation an implicit general solution in terms of a, can be written in the form x+ Transforming back to the variables and y the above equation becomes x+ Next using the initial condition y(0)=0 we find C= Then, after a little algebra, we can write the unique explicit solution of the initial value problem as y = - C. = C.