- #1

karush

Gold Member

MHB

- 3,269

- 5

$\displaystyle y^\prime - 2y = t^2 e^{2t}$

Obtain $u(t)$

$\displaystyle u(t)=\exp\int -2 \, dx =e^{-2t}$

Multiply thru with $e^{-2t}$

$e^{-2t}y^\prime

+ 2e^{-2t}y

= t^2 $

Simplify:

$(e^{-2t}y)'= t^2$

Integrate:

$\displaystyle e^{-2t}y=\int t^2\, dt=-\frac{t^3}{3}+c_1$

Divide thru by $e^{-2t}$

$\displaystyle -\frac{t^3e^{2t}}{3}+c_1e^{2t}$

ok took me 2 hours hope it ok

any suggest?

$$\tiny\textbf{Text: Elementary Differential Equations and Boundary Value Problems}$$