1 Solve the differential equation a dydx xy21x2Solutionans

1. Solve the differential equation :

a) dy/dx = xy^2/(1+x^2)

Solution

ans)

So you get xdx=dy/y^2

Integrate both sides

x^2/2=-1/y +c, x=1, y=1, so we get (1)^2/2=-1^-1 +c
1/2=-1+c, so c=3/2

Rearrange in terms of x. yx^2/2=-1 +3y/2, (times both sides by y, adding in the constant)

yx^2/2-3y/2=-1, y(x^2/2-3/2)=-1,
y=-1/(x^2/2-3/2)
y=-2/(x^2-3)

I was having trouble working out if it mattered what side you put the constant on, but its turns out my answer and the one above are the same:

y=-2(x^2-3) = 2/(3-x^2)