(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 (36.76 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 vax+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 = solve the initial value problem. y = 3 sin(3x + y) We obtain the following separable equation in the variables and v v A+ 1-sin(v) 1-sin(v) NOTE In order to carry out the required integration you might find it useful to multiply by cos² (u) = 1-sin² (v). Solving this equation and transforming back to the variables and y an implicit solution can be written in the form C 3x + y to and use