Solve this differential eqn:-
x(1-x^2)dy + (2x^2y-y-ax^3)dx
Answers
Simplifying
x(1 + -1x2) * dy + (2x2y + -1y + -1ax3) * dx = 0
Reorder the terms for easier multiplication:
x * dy(1 + -1x2) + (2x2y + -1y + -1ax3) * dx = 0
Multiply x * dy
dxy(1 + -1x2) + (2x2y + -1y + -1ax3) * dx = 0
(1 * dxy + -1x2 * dxy) + (2x2y + -1y + -1ax3) * dx = 0
(1dxy + -1dx3y) + (2x2y + -1y + -1ax3) * dx = 0
Reorder the terms:
1dxy + -1dx3y + (-1ax3 + 2x2y + -1y) * dx = 0
Reorder the terms for easier multiplication:
1dxy + -1dx3y + dx(-1ax3 + 2x2y + -1y) = 0
1dxy + -1dx3y + (-1ax3 * dx + 2x2y * dx + -1y * dx) = 0
Reorder the terms:
1dxy + -1dx3y + (-1adx4 + -1dxy + 2dx3y) = 0
1dxy + -1dx3y + (-1adx4 + -1dxy + 2dx3y) = 0
Reorder the terms:
-1adx4 + 1dxy + -1dxy + -1dx3y + 2dx3y = 0
Combine like terms: 1dxy + -1dxy = 0
-1adx4 + 0 + -1dx3y + 2dx3y = 0
-1adx4 + -1dx3y + 2dx3y = 0
Combine like terms: -1dx3y + 2dx3y = 1dx3y
-1adx4 + 1dx3y = 0
Solving
-1adx4 + 1dx3y = 0
Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right.
Add '-1dx3y' to each side of the equation.
-1adx4 + 1dx3y + -1dx3y = 0 + -1dx3y
Combine like terms: 1dx3y + -1dx3y = 0
-1adx4 + 0 = 0 + -1dx3y
-1adx4 = 0 + -1dx3y
Remove the zero:
-1adx4 = -1dx3y
Divide each side by '-1dx4'.
a = x-1y
Simplifying
a = x-1y