(b.) Consider the ordinary differential equation in (t > 0) ty" – (t+1)y' + y =0 Note that Y1(t) = et is a solution of this equation. (i). Write y(t) = v(t)e* and derive a differential equation v(t). Solution: • +(1 – ) • = 0 (ii). Solve the equation for v(t) you derive in (a). Solution. • c1( exp( )+ exp(-t)) + c2 (iii). Write out an expression for the general solution of the original ordinary differential equation. Solution: The general solution for y is y(t) = c1( )+c2 exp( ).

(b.) Consider the ordinary differential equation in (t > 0) ty" – (t+1)y' + y =0 Note that Y1(t) = et is a solution of this equation. (i). Write y(t) = v(t)e* and derive a differential equation v(t). Solution: • +(1 – ) • = 0 (ii). Solve the equation for v(t) you derive in (a). Solution. • c1( exp( )+ exp(-t)) + c2 (iii). Write out an expression for the general solution of the original ordinary differential equation. Solution: The general solution for y is y(t) = c1( )+c2 exp( ).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 15E: Find the general solution for each differential equation. Verify that each solution satisfies the...

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