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

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1 Point In Case An Equation Substitution U A Is In The Form Y F Ar By C I E The Rhs Is A Linear Function Of And 1 (29.62 KiB) Viewed 30 times

(1 point) In case an equation substitution u= a is in the form y'= f(ar+by+c), i.e., the RHS is a linear function of and y. We will use the +by+c to find an implicit general solution. The right hand side of the following first order problem is a linear function of x and y. Use the substitution u = x - y to solve the initial value problem. y' = e(-) + 1, y(2) = 2 We obtain the following separable equation in the variables and u: u' = Solving this equation and transforming back to the variables and y we arrive at the implicit solution = -x + C Finally we obtain the explicit solution of the initial value problem as y=