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

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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 X And Y We Will 1 (50.02 KiB) Viewed 31 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 x 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 and y. Use the substitution v = 2x + y to solve the initial value problem. 2 sin(2x + y) We obtain the following separable equation in the variables x and v: y' = x + v = 1 - sin(v) 1 - sin(v) 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 and use cos² (v) = 1 – sin² (v).