y'' + 2y' + y = x + e^(-x) , y(0)=0 , y'(0)=0 Solve the following 2nd ODE and find y(x)
Solve the following initial value problem 1 2 3 4 01 63 0 012 x +e' 0001 o x(0)0 Solve the following initial value problem 1 2 3 4 01 63 0 012 x +e' 0001 o x(0)0
Solve the following ODEs. x" + x = cost, x(0) = 0, x"(0) = 0 X" 2x = e x(0) = x'(0) = 0. Hint: Do not try to compute the Laplace trasform of e-42
Solve e^x dy/dx = x sec (y) y (0) = pi
x = x 2 e-t, with the initial condition X (0)-1 (solve with Separation of Variables method)
2. Solve the DE: (3x²y + cos x) dx +(x +e") dy = 0
4. (*) Solve the Cauchy problem Ut = 3Uxx, X E R, t> 0, u(x,0) = Q(x), x E R, for the following initial conditions and write the solutions in terms of the erf function. LS 2, -4 < x < 5 (a) $(x) = { 0, otherwise. (b) (x) = e-la-11 Note: In (b) complete the square with respect to y in the exponent of e to obtain a nice form. You need to split your integral based on...
Solve the following differential equation on the interval (0, oo) with conditions lim y(e) im y(x)-0 x→0+ y(z) = 0 an and Write your answer by Bessel functions Solve the following differential equation on the interval (0, oo) with conditions lim y(e) im y(x)-0 x→0+ y(z) = 0 an and Write your answer by Bessel functions
Solve the initial value problem. 7 dy + 9y - 9 e-X = 0, y(0) = dx 8 The solution is y(x) =
P3. Solve the equation au(t, x) = kazu(t, x)-γυ(t, x) a(0, r) = f(x) f or-00 < x < oo with f E L(R), where k > 0 and γ E R. P3. Solve the equation au(t, x) = kazu(t, x)-γυ(t, x) a(0, r) = f(x) f or-00