Ordinary Differential Equation problem Consider the ODESolut

(Ordinary Differential Equation problem)

Consider the ODE

This is a linear homogeneous equation with constant coefficients so solution is of the form

y=exp(kx)

Substituting gives

k^2-2k+1=0

k=1

So,

y1=e^{t},y2=te^{t}

ii)

y1(0)y1, y2(0)y2

iii)

General solution is

y=Ay1+By2=Ae^{t}+Bte^{t}

y(0)=A=1

y\'(t)=e^t+Be^t+Bte^t

y\'(0)=1+B=1

B=0

y= e^{t}