1.Solve the following initial value problems. (a) y\'\'- y\'- 2y = 0; y(0) = 1;

Question

1.Solve the following initial value problems. (a) y''- y'- 2y = 0; y(0) = 1; y'(0) = 2 (b) y''- 4y'-5y = 0; y(1) = 1; y'(1) = 1 (c) y'' + 25y = 3; y(0) = 1; y'(0) = 1 (d) y''-2y' + 17y = 0; y(0) = 2; y'(0) = 3 2.Solve the following differential equations using the method of undetermined coecients. That is, solve the related homogeneous equation and then look for a particular solution. (a) y'' + y'-12y = 24 (b) y''= -4y + 3 (c) y'' + 3y'+ 2y = -3e^-4t (d) y'' + 2y'+ 2y = 2 cos 2t (e) y'' + 4y' + 4y = 4 - t (f) y''- 2y' + y = t^2 (g) y' - 2y = e^2t (h) y' - 3y' + 2y = e^2t

Explanation / Answer

1)a)e^(2x)

b)1/3*e^(5x-5)+2/3*e^(1-x)

c)sin(5x)/5+22cos(5x)/25+3/25

d)e^x*(sin(4x)/4+2cos(4x))

2)a) pe^(-4x)+qe^(3x)-2

b) psin(2x)+qcos(2x)+3/4

c) pe^(-2t)+qe^(-t)+0.5e^(-4t)

d)

e)pte^(-2t)+qe^(-2t)+(5-t)/4

f)pte^t+qe^t+t^2+4t+6

g)(p+t)e^(2t)

h)pe^t-0.5e^(2t)

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