# Tagged Questions

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### Integrating absolute value function

I'm working on a problem drawing phase plane diagrams in my applied mathematics course. I'm supposed to draw the phase line diagram of $x''+\vert x\vert=0.$ In the process, I get to the differential ...
2answers
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### Question regarding usage of absolute value within natural log in solution of differential equation

The problem from the book. $\dfrac{\mathrm{d}y}{\mathrm{d}x} = 6 -y$ I understand the solution till this part. $\ln \vert 6 - y \vert = x + C$ The solution in the book is $6 - Ce^{-x}$ ...
1answer
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### Separable first-order linear equation and absolute value removal

We can use the integral of $\frac{1}{x}$ in order to solve a separable first-order linear equation like this: $\frac{dy}{dt} + f(t) y = 0$ $ln |y| = \left(-\int f(t)\,dt\right) + C$ and then: ...
1answer
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### How to manage the absolute value on a differential equation $|T(x)'+A(T,x)+B(T,x)| = f(T,x)$

Hi everyone I need to solve an equation of this type: $|T(x)'+A(T,x)+B(T,x)| = f(T,x)$ with boundaries conditions. The absolute value is my problem. Of course without it, the solution of these is ...