Differential Equations Answers

2.2 Find the solution of the following couple of differential equations: x^ prime =4x-y and y^ prime =-4x+4y When t = 0, x(0) = 1 and y(0) = 1 .

2y' =3y+1 ; y(1) = 0 .

y" -5y' +4y=0 ;y(0)=1 and y' (0)=1 .

Solve the following equation of the form 1+p^2=qz

2e^x is a particular integral for y'-y=2e^x. Is it true or false. Give reasons for your answer

1/(xy²+y⁴) is an integrating factor for the differential equation (x²y+y²)dx+(y³-x³)dy=0. Is it true or false. Give reasons for your answer

(D+D'-2)Z = 0

u_t -ku_xx = F(x, t) 0<x<l t>0

u(x, 0)= f(x) for 0<x<l and u(0, t)= u(l, t)= 0 for t >0

Solve

u_t = u_xx 0<x<l, t>0

u(0, t)= u(l, t)= 0

u(x, 0)= x(l-x) , 0<=x<=l

Solve the Heat Equation du/dt=40d²u/dx² Subject to the conditions

u(0,t)=0, u(π,t)=0

u(x,0)=5sinx-2sin5x