Question

Solve the following differential equation (x^2+xy)dy=(x^2+y^2)dx

Answer 1

Let's solve for d.

(x2+xy)(d)y=(x2+y2)(d)x

Step 1: Add -dx^3 to both sides.

dx2y+dxy2+−dx3=dx3+dxy2+−dx3

−dx3+dx2y+dxy2=dxy2

Step 2: Add -dxy^2 to both sides.

−dx3+dx2y+dxy2+−dxy2=dxy2+−dxy2

−dx3+dx2y=0

Step 3: Factor out variable d.

d(−x3+x2y)=0

Step 4: Divide both sides by -x^3+x^2y.

d(−x3+x2y)/−x3+x2y=0/−x3+x2y

d=0/−x+y

Answer:

d=0/−x+y


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