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Find the general solution of the following differential equations using method of undetermined coefficients: (i) y''−2y'+y =x2e5x,


Solve the following initial value problems using method of undetermined coefficients: (i) y''−9y = ex+x−1, y(0) = −1,y'(0) = 1,


Solve the following initial value problems using method of undetermined coefficients: (ii) y''+y' = 5xsinx, y(0) = 0,y(0) = 1.


Solve the following initial value problems using method of undetermined coefficients: (i) y−9y = ex+x−1, y(0) = −1,y(0) = 1,


Use variation of parameter methods to find the particular solution of xy−(x+1)y+y = x2, given that y1(x) = ex and y2(x) = x + 1 form a fundamental set of solutions for the corresponding homogeneous differential equation.


The probability of getting at most two heads when three coins are tossed simultaneously.

The probability of getting at most two heads when three coins are tossed simultaneously.

The probability of getting a sum divisible by three if a pair of fair dice is rolled and the numbers that turn up are noted.

1. A school organized a fundraising activity for its donations to victims of a recent typhoon. It involves selling 1000 raffle tickets. One ticket costs $100. The lone winner of this raffle will receive free tuition worth $30,00. What is your expected net gain if you buy one raffle ticket?




1. A school organized a fundraising activity for its donations to victims of a recent typhoon. It involves selling 1000 raffle tickets. One ticket costs $100. The lone winner of this raffle will receive free tuition worth $30,00. What is your expected net gain if you buy one raffle ticket?




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