Recent content by Dr.Doom

Homework Statement I am trying to show that the average solar irradiance over Earth's surface is 1/4 of the total solar irradiance using only calculus. Homework Equations Solar Irradiance = S_{o} Irradiance = F = S_{o}cos(θ) The Attempt at a Solution Using geometry, I can easily...

I'm having trouble seeing how it comes out to (1+v)/(1-v2-2v)

Ok, so I rewrite it as \frac{1}{x}dx=\frac{1+v}{1-v}-\frac{1}{v}dv. Do I need to do an additional substitution on \frac{1+v}{1-v}?

Homework Statement Find the general solution of the differential equation: (x+y)y'=x-y Homework Equations I want to solve this as a homogeneous differential equation, so our equations are: v=\frac{y}{x}, y=vx, \frac{dy}{dx}=v+x\frac{dv}{dx} The Attempt at a Solution I...

Thanks for the help, guys!

Well, it's an initial value problem so I'm thinking there's something more to it. The textbook gives the answer as y(x)=-1+ex+x2/2

-(1+x) is the coefficient of y. I went back and corrected this but I am still ruining into a problem when integrating the right hand side of my function: (1+x)e-x-(x2/2)

Homework Statement y'=1+x+y+xy, y(0)=0Homework Equations \frac{dy}{dx}+P(x)y=Q(x) \rho(x)=e\int(P(x)dx)The Attempt at a Solution My main problem is correctly getting it into the form, \frac{dy}{dx}+P(x)y=Q(x). I know what to do from there. First, I tried y'-(y+xy)=1+x, where P(x)=1+x...