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dP/dt+2tP=P4t-2
(1+x)dy/dx-xy=x+x^2
Let A(t), t in I be a real matrix. Prove that (5.6.31) can also be written as Psi(t)= Phi(t) int t 0^t Psi^ T (s)b(s)ds. (i) t in I provided Psi ^ T* (t) * Phi * (t) = E; Psi(t)=( Psi^ r^"-1")^ Tint 10^t Psi^ T (s)b(s)ds, (ii) t in I, where is a fundamental matrixfor the adjoint system x^ prime =-A^ T (t)x.
In 2000, the population of a country was 4U million. I he population was growing at a rate of 5% per year and every year 30 000 people emigrated from the country. 6.1 Write down an initial value problem for the population P. (1 pt) 6.2 Solve the initial value problem. (2 pts) 6.3 Estimate the population in 2010
y''+y=sin^2(x)
Find the general solution to y"-y'-2y=2e^3x
Find the general solution to y"+4y'+3y=x
