# Tagged Questions

Questions on (ordinary) differential equations. For questions specifically concerning partial differential equations, use the (pde) tag.

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### How to integrate the following: $\int{\frac{2y'y}{y^2+1}dx}$

I have encountered the following problem: $\int{\frac{2y'y}{y^2+1}dx}$ According to wolfram the solution is: $log(y^2 + 1)$ How was this solution derived and which rules were used?
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### How do you solve the following separable differential equation: y'y = y + 1?

I just started learning about differential equations and encountered following equation: $$y'y = y +1$$ Wolfram alpha provided the following explanation: here But I'm not sure how the integration ...
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### Solving ODE for practice

I'm doing self study and I can't solve this equation: $$ax + \ln y = y + b$$ Where I'm supposed to eliminate the arbitrary constants. The given answer is $(y - y^2)(y'') = (y')^2$ But my workings ...
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### Singularities in a PDE

This is more of a general question rather than anything specific but I was just wondering if someone could point me toward resources which discuss singularities in a PDE rather than in an ODE (by ...
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### How small need it be to approximate integral as one area of product of initial value times length.

$$\left(\int_{t}^{t+\Delta t}a(t')dt'\right), a(t) \text{ is scalar}$$ How small need $\Delta t$ be to approximate $$\left(\int_{t}^{t+\Delta t}a(t')dt'\right)$$ as $$a(t)\Delta t$$ [ Just one ...
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