In solving this problem, derive the general solution of the given
equation by using an appropriate change of variables.
1. ∂u/∂t – 2 ∂u/∂x = 2
Answer: u(x,t) = f(x + 2t) – x
ic curves, and (b) check you answer by plugging it back into the
equation.
2. ∂u/∂x + x2 ∂u/∂y = 0
Answer: (a) u(x,y) = f(1/3 x3 – y)
Mathematics Homework Solutions
#162141
Solving Partial Differential Equations by Change of Variables and Characteristic Curves
In solving this problem, derive the general solution of the given equation by using an appropriate change of variables.
1. ∂u/∂t - 2 ∂u/∂x = 2
Answer: u(x,t) = f(x + 2t) - x
In this exercise, (a) solve the given equation by the method of characteristic curves, and (b) check you answer by plugging it back into the equation.
2. ∂u/∂x + x2 ∂u/∂y = 0
Answer: (a) u(x,y) = f(1/3 x3 - y)
Solving Partial Differential Equations by Change of Variables and Characteristic Curves is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
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