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

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1 Point In Case An Equation Is In The Form Y F Ax By C I E The Rhs Is A Linear Function Of A And Y We Will Use 1 (37.38 KiB) Viewed 14 times

(1 point) In case an equation is in the form y' = f(ax+by+c), i.e., the RHS is a linear function of a and y. We will use the substitution v= ax +by+c to find an implicit general solution. The right hand side of the following first order problem is a linear function of a and y. Use the substitution v= x - y to solve the initial value problem. y We obtain the following separable equation in the variables and v: = Y sin²(2-y), y(1) = 1 = Solving this equation and transforming back to the variables x and y we arrive at the implicit solution = x + C Finally we obtain the explicit solution of the initial value problem as