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

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1 Point In Case An Equation Is In The Form Y F Ax By I E The Rhs Is A Linear Function Of X And Y We Will Use 1 (48.9 KiB) Viewed 55 times

(1 point) In case an equation is in the form y' = f(ax + by), i.e., the RHS is a linear function of x and y. We will use the substitution v = ax + by 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 v = x + y to solve the initial value problem. = sin(x + y) y' v' = We obtain the following separable equation in the variables x and v: 1 - sin(u) 1 - sin(u) Solving this equation and transforming back to the variables x and y an implicit solution can be written in the form = C NOTE In order to carry out the required integration you might find it useful to multiply by x + and use cos² (u) = 1 - sin² (u).