# Questions tagged [singular-solution]

For questions about the singular solution of the ordinary differential equations. It is a special type of solution different from general solution. Such solutions does not contain any arbitrary constant and is not a particular case of the general solution.

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### Types of singularities in ODE

Consider the nonlinear ODE $$y\cdot\frac{d^{2}y}{dx^{2}}-\left(\frac{dy}{dx}\right)^{2}+1=0$$ with $y : \mathbb{R} \to \mathbb{R}$. As seen, it does not satisfy Picard–Lindelöf theorem because of ...
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### It is possible to find a solution to $y''+\sqrt{|y|}\operatorname{sgn}(y)+\sqrt{|y'|}\operatorname{sgn}(y')=0,$ $\,y'(0)=0,\,y(0)= 1/4$?

It is possible to find an exact solution (hopefully in "close form") to $$y''+\sqrt{|y|}\operatorname{sgn}(y)+\sqrt{|y'|}\operatorname{sgn}(y')=0, \,y'(0)=0,\,y(0)= 1/4$$? How?... There ...
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### The differential equation $y'=y+1$ has no singular solution?

$\frac{dy}{dx}=y+1$ Solving the above given differential equation, yields the following general solution. $y+1=e^{x+C}$ $y=Ce^{x}-1$ $\implies$ Solution $y=-1$ at $C=0$ Can I say that $y= -1$ is a ...
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### How to solve : $(3x+5)\Big(\frac{\mathrm{d}y}{\mathrm{d}x}\Big)^2-(3y+x)\Big(\frac{\mathrm{d}y}{\mathrm{d}x}\Big)+y=0$? [closed]

How to solve this ordinary differential equation? $$(3x+5)\Big(\frac{\mathrm{d}y}{\mathrm{d}x}\Big)^2-(3y+x)\Big(\frac{\mathrm{d}y}{\mathrm{d}x}\Big)+y=0$$ How to find the general solution and ...
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I have the following SL problem: $$(x^{2} f')'+ \lambda f = 0$$ where $\lvert f(x) \rvert$ is bounded as $x \rightarrow 0$ and $f(1) = 0$ I have to show that the above problem has NO ...