Need Help On Initial Value Problems

[vpathak]

Hi, I have a Calculus test coming up and am very confused on how to start approching these types of problems (initial value problems) If possible can someone work these 2 different types of problems out and show some work so I know how to proceed with the rest of them? I don't think they are that hard, for some reason I'm just confused. Thanks


Problem 1: y' +ty = t, y(0) = 0

Problem 2: y' = y^2*sint, y(0) = 1

Thanks again for all those who help!

 

[Alem2000]

I don't think anyone will help you on here unless you show what you did sorry but that's how it works

 

[vpathak]

well I am just lost in even how to attempt these types of problems, so yeah...i hope someone does

 

[Alem2000]

They arnt that hard, read the book and try some examples. Then try it and if you don't get far post what you did and people will tell you what you need to fix.

 

[ReyChiquito]

these are separable equations, your main goal must be put all the y's in one side and all the t's in the other and then integrate. For example, on 1

y'+ty=t ,y(0)=0 =>
y'=t-ty =>
y'=t(1-y) =>
y'/(1-y)=t => using y'=dy/dt

dy/(1-y)=t dt

then integrate both sides. Check any differential equations book. Look for separable equations.

 

[vpathak]

thanks i think i got it.