Assignment of differential equation It should be neat embedded in file cover Assignment folder Otherwise 0 Marks

Q#1:

x^3-3x^2y=c 
3x^2 dx-3(2xydx+x^2dy)=0
3x^2 dx-6xy dx-3x^2 dy=0
 Divide by 3x
xdx-2ydx-xdy=0
xdx-2ydx-xdy=0
(x-2y)dx-xdy=0



Q#3:
Solution for (x^5+3y)dx-xdy=0 equation:

Simplifying
(x5 + 3y) * dx + -1xdy = 0

Reorder the terms for easier multiplication:
dx(x5 + 3y) + -1xdy = 0
(x5 * dx + 3y * dx) + -1xdy = 0

Reorder the terms:
(3dxy + dx6) + -1xdy = 0
(3dxy + dx6) + -1xdy = 0

Reorder the terms:
3dxy + -1dxy + dx6 = 0

Combine like terms: 3dxy + -1dxy = 2dxy
2dxy + dx6 = 0

Solving
2dxy + dx6 = 0

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), 'dx'.
dx(2y + x5) = 0



Q#4:

Solution for vdx+(2x+1-vx)dv=0 equation:

Simplifying
vdx + (2x + 1 + -1vx) * dv = 0

Reorder the terms:
dvx + (1 + -1vx + 2x) * dv = 0

Reorder the terms for easier multiplication:
dvx + dv(1 + -1vx + 2x) = 0
dvx + (1 * dv + -1vx * dv + 2x * dv) = 0

Reorder the terms:
dvx + (1dv + 2dvx + -1dv2x) = 0
dvx + (1dv + 2dvx + -1dv2x) = 0

Reorder the terms:

1dv + dvx + 2dvx + -1dv2x = 0

Combine like terms: dvx + 2dvx = 3dvx
1dv + 3dvx + -1dv2x = 0

Solving
1dv + 3dvx + -1dv2x = 0

Solving for variable 'd'.


Move all terms containing d to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), 'dv'.
dv(1 + 3x + -1vx) = 0


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