Reference no: EM132276098

Questions -

Q1. Find y in each of the following:

(a) y = cos3x∫sin3x tan3x dx

(b) y = ∫x/(x²+1) dx

(c) y = ∫1/(x²+1) dx

Q2. Show that d/dx (e^0.196xy) = e^0.196x dy/dx - 0.196e^0.196xy.

Q3. Given that d/dx(e^xy) = Ae^by, find y.

Q4. Given that df(x, y)/dy = 2x²y - 6;

Show that f(x, y) = x²y² - 6y + n(x).

Q5. Given the equation: d/dx + P(x)y = 9(x)yⁿ.

Show that dz/dx = (1 - n)y^-n dy/dx; where z = y^1-n.

Q6. (a) Verify that y(6) = ¾ + c/t² is the general solution of 2t dy/dt + 4y = 3.

(b) What is the actual solution to the following interval value problem (1VP):

2t(dy/dt) + 4y = 3, y(1) = -4.

Q7. (a) Show that y² = t² - 3 is the actual implicit solution of dy/dt = t/y, y(2) = -1.

(b) Find an actual explicit solution of the above differential equation.

Attachment:- Assignment Files.rar