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2.2. Solve the ivp sin(x) dx + y dy = 0, where y(0)

2.1. Solve 2xy + 6x + (x^2 - 4)y'=0

Derive one dimensional heat equation, explaining all the variables and constant as

well as stating all necessary assumptions made.

Find the general solution of the given differential equation.

y' + 3x2y = x2

(b) A consumer has a utility function of the form; U = X.Y Where Xand Y are any two goods. Given further that; The price of goodsX (Px) = Kshs. 8 The price of good Y (Py) = Kshs. 20 Theconsumers income (I) = Kshs. 1000

(i) Calculate the number of units that the consumer should consume in order to maximize utility. (10 marks)

(ii)What is the maximum utility the consumer derives from the consumption of the two goods. (2 marks)

xdy/dx = x2 +5y

dx dt=2x-4y 

dx dt=2x+4y


Undetermined Coefficients

4. y^ prime prime +2y^ prime +5y=1+e^ x