Solve the differential equation
a) e^x (dy/dx)=1-2(e^x)y
For this one i divided by e^x to get dy/dx= 1/e^x -2y
which equals dy/dx-2y= 1/e^x
I think you are supposed to find an integrating factor. then go on to simplify.
b) 1+x (dy/dx)+y= sqrt(x)
for this one dy/dx=sqrt (x)/(1+x) -y/ (1+x) which equals dy/dx+(y/(1+x))= sqrt (x)/(1+x)
Similar to above I am obviously having trouble determining the integrating factor.
c) t (dy/dt)+2y=t^3
I also couldnt figure out the operating factor other ones worked out other than these ones. dy/dt+ (2y/t)= t^2
d) x (dy/dx) +y= sin x (x>0)
so, dy/dx+(y/x)= sinx/x
integrating e^ (int P(x)dx=e^(int 1/x)= e^lnx=x
so d/dx (xy)=sinx integrating both sides gives xy= -cosx+c
i am not sure if i did any of this right. Any help on all or even one of the question will be appreciated. Exam is in 2 days and I really am trying to get this all in my head ... p.s. For people who think i didn't try to solve this, believe me when i say i spent hours trying to figure these differential questions by reading notes and internet.