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Differential Equations
an airplane headed 30 degrees northeast climbing on a 20 degrees incline at a speed of 240 miles per hour passes 1 mile directly over a car headed south on a flat road at the rate of 60 miles per hour at what rate of speed are they separating after 10 minutes?
Differential Equations
Please solve the following IBVP:
u_tt = u_xx on 0<x<pi, t>0.
u(0,t) = 0, t >= 0.
u(pi,t) = 0, t>= 0.
u(x,0) = sin^3(x) 0<=x<=pi.
u_t(x,0) = sin(2x) 0<=x<=pi.
u_tt = u_xx on 0<x<pi, t>0.
u(0,t) = 0, t >= 0.
u(pi,t) = 0, t>= 0.
u(x,0) = sin^3(x) 0<=x<=pi.
u_t(x,0) = sin(2x) 0<=x<=pi.
Differential Equations
Find the canonical form of the following PDE:
u_xx - 6u_xy + 9u_yy = xy^2
**Be sure to show the change of coordinates that reduces the PDE to canonical form.
u_xx - 6u_xy + 9u_yy = xy^2
**Be sure to show the change of coordinates that reduces the PDE to canonical form.
Differential Equations
find formal simplified equivalent expressions for cost+sint.∂t and 1+2et∂(t-1)
Differential Equations
Differentiate
tan((x^2) y-x) = x
tan((x^2) y-x) = x
Differential Equations
a grape 1 cm in diameter that is initially at a uniform temperature of 20 C is placed in a refrigerator such that k=0.003,using law of cooling find the T after 10 minutes?
Differential Equations
If u is a solution of u_tt -c^2u_xx = 0 on -infinity < x < +infinity, t >0 for which u-->0, u_x-->0, u_t-->0 as x--> +,- infinity, then E = integral from -inf to +inf (u^2_t + c^2u^2_x)dx is constant.
Does there exist a corresponding conservative quantity E* for solutions of the equation:
u_tt - c^2u_xx - bu = 0?
Does there exist a corresponding conservative quantity E* for solutions of the equation:
u_tt - c^2u_xx - bu = 0?
Differential Equations
a grape 1 cm in diameter that is initially at a uniform temperature of 20 C is placed in a refrigerator such that k=0.003,using law of cooling find the T after 10 minutes?
Differential Equations
form a PDE by elimination f and g from z= f(x2-y)+g(x2+y)
Differential Equations
Given an ODE, let x: I -> R^n be a solution defined on an interval I, a subset of R. A phase curve in R^n is the image x(I) where x is a solution to the ordinary differential equation. Consider the ODE:
dx/dt = x
dy/dt = ky (1)
where k is a constant. Giving a detailed answer: Is the curve give by |y| = C|x|^k where C is a constant, a phase curve of the ODE (1)?
dx/dt = x
dy/dt = ky (1)
where k is a constant. Giving a detailed answer: Is the curve give by |y| = C|x|^k where C is a constant, a phase curve of the ODE (1)?
