(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 (38.57 KiB) Viewed 13 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+e 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=3z-y + 1 to solve the initial value problem. y = 3e3-y+¹) +3, y(0)=1 We obtain the following separable equation in the variables and u Solving this equation and transforming back to the variables a and y an implicit solution can be written in the form = C 3x + From this formula and the initial condition we can compute C = Finally we obtain the explicit solution of the initial value problem as Y =