Differential Equations Answers

Give the general solution using determination of

Integrating Factors.

1. (x^2 + y^2 + 1)dx + x(x − 2y)dy = 0

2. y(4x + y)dx − 2((x^2 − y)dy = 0

3. y(y + 2x − 2)dx − 2(x + y)dy = 0

4. y(8x − 9y)dx − 2x(x − 3y)dy = 0

5. y(2x^2 − xy)dx − (x − y)dy = 0

6. 2(2y^2 + 5xy − 2y + 4)dx + x(2x + 2y − 1)dy = 0

7. (2x^2 + 3xy − 2y + 6x)dx + x(x + 2y − 1)dy = 0

2e^-x + e^y = 3^x-y at 0,0

v=11sin4t-5cos5t

(2xz-yz)dx+(2yz-zx)dy-(x2-zx+y2)dz=0

find the integral surface of the equation (x-y)y^2*p + (y-x)x^2*q = (x^2+y^2)z through the curve xz = a^3 and y = 0

find the general solution of the equation 2x(y+z^2)p + y(2y+z^2)q = z^3. and deduce that

yz(z^2+yz-2y) =x^2 is a solution.

solve dx/2x(y+z^2) = dy/y(2y+z^2) = dz/z^3 find two solutions

solve dx/(x-y)y^2 = dy/(y-x)x^2 = dz/x^2+y^2

In orthogonality of legendre polynomials, why the limits of integral is from -1 to 1

Why integral t²(-e^-t) with limits t= 0, ∞ becomes zero.