V PONS In case an equation is in the form y' = f(ar +by+ c), i.e., the RHS is a linear function of er and y. We will use

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V Pons In Case An Equation Is In The Form Y F Ar By C I E The Rhs Is A Linear Function Of Er And Y We Will Use 1 (26.55 KiB) Viewed 30 times

V PONS In case an equation is in the form y' = f(ar +by+ c), i.e., the RHS is a linear function of er and y. We will use the substitution = ax +by+c to find an implicit general solution The right hand side of the following first order problem V = (3x - 4y + 1)3/4 + (0) = 0 is a function of a linear combination of er and y. i.e. ' = fax +by+c). To solve this problem we use the substitution v = ax + by + c which transforms the equation into a separable equation We obtain the following separable equation in the variables x and u: u Solving this equation an implicit general solution in terms of u can be written in the form Transforming back to the variables and the above equation becomes C Next using the initial condition y(0) = 0 we find C Then, after a little algebra, we can write the unique explicit solution of the initial value problem as V