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2017-01-15 Differential Equations - Solve for x:

Hello John,    This cannot be solved for analytically in terms of elementary functions.    I did solve it numerically to obtain a very good approximation.  x=-40.7459009034... The attached graph shows

2017-01-13 Advanced Math - linear algebra:

I think the trace of X should be zero. Here's my derivation:    Traces have some simple and useful properties, such as (for a matrices A and B)    1. Tr(A +B) = Tr(A) + Tr(B)    2. Tr(A) = Tr(A^t)    3

2017-01-09 Differential Equations - ODE:

Hello Giulia,    As far as I know, this has no general solution in terms of elementary functions.    A computer algebra system (Maple) gives the following result:  y(x) = KummerM((1/2)*e/b, 1/2, b*(d-x)^2/a^2)*_C2+KummerU((1/2)*e/b

2017-01-07 Number Theory - Joint Proportionality:

Hello Kenneth  I misunderstood your question.  It is the number of gallons that is the dependent variable which is directly proportional to the number of miles and to the number of trips.  g = kmt, so

2017-01-07 Basic Math - Determing actual age from apparent age of characters:

Hello Julian,    Without additional info there are literally infinitely many possibilities!  The relationship could be (1) linear, (2) quadratic, (3) cubic, (4) exponential, (5) logarithmic,  (6) power

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