Question

In: Advanced Math

Solve the following initial value problems and graph the solutions at times t = 1, 2,...

Solve the following initial value problems and graph the solutions at times t = 1, 2, and 3:
(a) u_t − 3u_x = 0, u(0, x) = e^−x^{2}
(b) u_t + 2u_x = 0, u(−1, x) = x/(1 + x^2)
(c) u_t + u_x + 1/2u = 0, u(0, x) = tan^−1 x;
(d) u_t− 4u_x + u = 0, u(0, x) = 1/(1 + x^2)\

Solutions

Expert Solution


Related Solutions

3) Solve the initial value problems c) R′ + (R/t) = (2/(1+t2 )) , R(1) =...
3) Solve the initial value problems c) R′ + (R/t) = (2/(1+t2 )) , R(1) = ln 8. e) ) cos θv′ + v = 3 , v(π/2) = 1. 5) Express the general solution of the equation x ′ = 2tx + 1 in terms of the erf function. 7) Solve x ′′ + x ′ = 3t by substituting y = x ′ 9) Find the general solution to the differential equation x ′ = ax + b,...
Solve the following initial value problems (1) dy/dt = t + y y(0) = 1 so...
Solve the following initial value problems (1) dy/dt = t + y y(0) = 1 so y(t) = (2)  dy/dt = ty y(0) = 1 so y(t) =
1. solve the initial value problem. (t^(2)+1)y'+2ty=tant , y(0)=2 2.find the solution to this initial value...
1. solve the initial value problem. (t^(2)+1)y'+2ty=tant , y(0)=2 2.find the solution to this initial value problem. yy'=e^x+x , y(0)=y_0 y_0 is a nonzero constant.
8. Find the solutions of the following initial value problems • x ''' + 6x ''...
8. Find the solutions of the following initial value problems • x ''' + 6x '' + 12x ' + 8x = 0, x(1) = −2, x' (1) = x '' (1) = 0 • x ^(5) + 4x^ (4) + 5x^ (3) = 0, x(0) = x ' (0) = x '' (0) = 1, x^(3) (0) = x^ (4) (0) =0
Solve listed initial value problems by using the Laplace Transform: 3.      yll + 4y = t −...
Solve listed initial value problems by using the Laplace Transform: 3.      yll + 4y = t − 1,    y(0) = 1, yl(0) = −1
Solve the following initial value problem over the interval from t = 0 to 2 where...
Solve the following initial value problem over the interval from t = 0 to 2 where y(0) = 1 using the following methods. dy/dt=y*t^2−1.1y a) Analytical method b) Euler's method with h=0.5 at t=2 c) Euler's method with h=0.25 at t=2 d) Midpoint method with h=0.5 at t=2 e) Fourth-order Runge-Kutta method with h=0.5 at t=2 f) Display all yor results obtained above on the same graph
Solve the given initial-value problem. X' = 1   −1 1   3 X + t t +...
Solve the given initial-value problem. X' = 1   −1 1   3 X + t t + 1 , X(0) = 9 8 X(t) =
Solve the following initial value problems by the method of undetermined coefficients: A.) y′′ + y...
Solve the following initial value problems by the method of undetermined coefficients: A.) y′′ + y = 4 sin t − cos t. B.) y′′ = 5t4 − 2t.
Solve the following initial value problems by the method of undetermined coefficients: A.) y′′ + y...
Solve the following initial value problems by the method of undetermined coefficients: A.) y′′ + y = 2 + sin t. B.) y′′ + 4y′ + 5y = e−2t(1 − cos t).
Solve the following initial value problem over the interval from t = 0 to 1 where...
Solve the following initial value problem over the interval from t = 0 to 1 where y(0) = 1 using the following methods with a step size of 0.25. dy/dt=(1+4t)*sqrt(y) a) Analytical method b) Euler's method c) Heun's method without iteration d) Ralston's method e) Fourth-order Runge-Kutta method f) Display all your results obtained above on the same graph
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT