I would divide both sides by giving
Now find an integrating factor
Multiply this guy through the equation and everything should start to piece together...
I need to solve the equation:
x (dy/dx) + 5y = 7x where y(1) = 7/2
The correct answer i have recieved is y = 7/6 (x + 2x^-5)
How do i get to this answer?
Ive been given this as a hint:
x (dy/dx) + ay = bx^n can be simplified by multiplying both sides by x^(a-1)
To give x^a (dy/dx) + a(x^(a-1))y = bx^(n+a-1)
Which can be written as d/dx((x^a)y)
But this doesnt seem to help me? Thanks
The equation is also Cauchy-Euler. You could assume a solution of the form and plug it into the DE to solve for
Cheers.