Analytic solution to the one-compartment model November 27    1

Analytic solution to the one-compartment model
I have the following linear system of ordinary differential equations:$$\frac {dA} {dt} = -k_a \cdot A$$ $$\frac {dC} {dt} = k_a \cdot A - k_0 \cdot C$$$$A(0) = A_0$$ $$C(0) = 0$$Some people ...

Implicit Derivative help November 27    2

The problem I'm working on is $\sin( x + y ) = 2x-2y$. If anybody could give a step by step solution I would be very appreciative. I'm trying to find the derivative of y$$\sin( x + y ) = 2x-2y$$ $$\cos(x+y)(1+y')=y'$$ $$\cos(x+y)+y'\cos(x+y)=y'

Lifting Trial Functions for Second Order ODES November 27    2

I have a general question here, I've been doing non-homogenous second order differential equations. As you know, sometimes when finding the particular integral, the general trial function already appears in the complimentary function and it is necess

IVP of second order linear ODE November 27    1

Bumps are often built into roads to discourage speeding. Consider a crude model of the vertical motion $y(t)$ of a car encountering the speed bump with the speed $V$ is given by $$y(t)=0 \qquad\text{for}\; t \leq -L/(2V)$$ $$my''+ky= \begin{cases} F_

Wronskian and finding a function November 27

$W[e^{2x},h(x)]$= $\begin{vmatrix} e^{2x} & h \\ 2e^{2x} & h' \\ \end{vmatrix}$ => $h'e^{2x}-2he^{2x}=3e^{4x}$$h'-2h=3e^{2x}$Integrating factor is $e^{-2x}$$e^{-2x}h(x)=3x+C$$h(x)=3xe^{2x}+Ce^{2x}$Is this correct?

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