Differential Equations Answers

w=dependent variable

v=independendt variable

w(2v-w+1)dv+v(3v-4w+3)dw=0

Given the equation below, solve for the general solutions.

w = dependent variable, v = independent variable

1. w (4v + w) dv - 2 (v^2 - w) dw = 0

Solve for the equation of the family of curves in which the slope is (5−𝑥)

(𝑦−3)

Determine the type of the curve and the equation of a member passing through

(2 − 1).

Find regular singular point of (x^2+1)y"+y'+y=0

INTEGRATING FACTOR

Test for exactness and find the general solution:

1. y(x² + y)dx + x(x² − 2y)dy = 0

2. (2y⁴ + 1)dx + 4xy³dy = 0

3. y(x³y − 1)dx + x(xy⁴ − 1)dy = 0

4. y²dx + xydy = 0

5. y(y − 1)dx + xdy = 0

EXACT DIFFERENTIAL EQUATIONS

Test for exactness and find the general solution:

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

2. (y + 2xy³)dx + (1+ 3x²y² + x)dy = 0

3. 3x²ydx + (x³ + 2y⁴)dy = 0

4. (1/y)dx - (x/y²⁾dy = 0

5. (4x³ − y³)dx − 3xy²dy = 0

Solve xp2-yp-y=0

Find the laplace transform of t^2?

Find the laplace transform of sinat where a is a constant

Find the laplace of cosat where a is a constant