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

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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 A And Y We Will Use Th 1 (35.62 KiB) Viewed 14 times

(1 point) In case an equation is in the form y'= f(ax+by), i.e., the RHS is a linear function of a and y. We will use the substitution v= az + by 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' = sin(x + y) We obtain the following separable equation in the variables z and v: v= = NOTE In order to carry out the required integration you might find it useful to multiply by cos² (u) 1-sin² (u). Solving this equation and transforming back to the variables and y an implicit solution can be written in the form 2+ 1-sin(u) and use 1-sin(u) = C