in case an equation is in the form y-f(az+by+c), ie, the RHS is a linear function of a and y. We will use the substituti

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In Case An Equation Is In The Form Y F Az By C Ie The Rhs Is A Linear Function Of A And Y We Will Use The Substituti 1 (19.16 KiB) Viewed 15 times

in case an equation is in the form y-f(az+by+c), ie, the RHS is a linear function of a and y. We will use the substitutioneaz+by+e to find an implicit general solution. The right hand side of the following first order problem -(42-49+1)+1, (0)-0 is a function of a linear combination of a and y. ie. -f(az+by+c) To solve this problem we use the substitutionar+by+cwhich transforms the equation into a separable equation We obtain the following separable equation in the variables z and e Solving this equation an implicit general solution in terms of z, t can be written in the form Transforming back to the vanables and y the above equation becomes 2+ 2+ Next using the initial condition y(0) 0 we find C Then, aber a te algebra, we can write the uneque explic solution of the initial value problem as -C