Assignment $5$: First$-$Order Differential Equations $-$ Particular Solutions

Instructions:

Solve each differential equation below.

Find the particular solution using the given initial condition.

Show all steps clearly.

Write your solutions neatly on A$4$ paper.

Problems:

$\frac{dy}{dx}2y=4e^{-x},y(0)=1$

$\frac{dy}{dx}=ycosx,y(0)=2$

$\frac{dy}{dx}=\frac{2xy}{1x^2},y(0)=3$

$\frac{dy}{dx}\frac{y}{x}=sinx,y()=0$

$(2xy{y}^2)dx{x}^{2}dy=0,y(1)=1$

$\frac{dy}{dx}=\frac{xy}{x-y},y(1)=1$

$\frac{dy}{dx}\frac{2y}{x}=x^2{y}^3,y(1)=1$