$(20$ P$)$

a$)y^{\text{'}}=\frac{2yx}{x}$ diferansiyel denkleminin $$z$$m$$nd$$ bulunuz.

b$)x{y}^{\text{'}}y=x{y}^3$ diferansiyel denkleminin $$z$$m$$n$$ bulunuz.

$(20$ P$)$

$y^{\text{'}\text{'}\text{'}}-3y^{\text{'}\text{'}}3y^{\text{'}}-y=e^{2x}1$ diferansiyel denkleminin $$z$$m$$n$$ bulunuz.

$(20$ P$)$

$y^{\text{'}\text{'}}-2y^{\text{'}}y=\frac{e^x}{x},y(1)=0,y^{\text{'}}(1)=1$ ba$$lang$$ de$$er probleminin $$z$$m$$na bulunuz.

$y(1)=0$

$y^{\text{'}}(1)=1$

$(20$ P$)$

$4.$ a$)L(5e^{2x}7e^{-x})=?$

$2$ soru Laplace

b$)L^{-1}\{\frac{s4}{s^{2}4s8}\}=?$

$(20$ P$)$

$5.y^{\text{'}\text{'}\text{'}}{y}^{\text{'}}=e^x,y(0)=y^{\text{'}}(0)=y^{\text{'}\text{'}}(0)=0,$ diferansiyel denklemini Laplace d$$n$$m$$ yard$$m$$yla $$z$$n$$z$.$