# Questions tagged [integrating-factor]

For questions about integrating factors in general as well as their application to solving ODEs.

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### How to solve this Differential equation(Integrating-factor)?

Can someone help me with this differential equation. $$y\tan(x) + \frac{e^{xy}}{\cos^2(x)} + x\tan(x)y' = 0$$ I guess it should be used integrating-factor but I can't solve it.
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### Using an Integrating Factor to solve differential equation

I am trying to solve $$(x^2y^3+y)dx+(x^3y^2-x)dy=0$$ First of all we check this equation for exactness $\frac{\partial P}{\partial y}=3y^2x^2+1$ $\frac{\partial Q}{\partial x}=3x^2y^2-1$ The ...
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### Why is this first-order ODE amenable to the method of integrating factor/separable?

Background We know that the first order differential equation in the form $$\frac{dy}{dx}+p(x)y=q(x)$$ is amenable to the method of integrating factor Question How is this first order equation ...
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### Integration factor method with constants of integration

The question at hand is a step in solving the manifolds of a non-linear dynamical system. However the part I need help with is a step using the integrating factor method. We need to solve the 1st ...
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### Transforming a partial derivative into a total derivative via integrating factor

Trying to solve an ordinary differential equation of the type: $y^{\prime}+P(x) y=Q(x)$ Wikipedia states: "To derive this, let $M_{(x)}$ be the integrating factor of a first order linear differential ...
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### Common integrating factor of two differential equations.

The following differential equations have a common integrating factor. $$(3y+4xy^2)dx+(4x+5x^2y)dy=0$$ $$(6y+x^2y^2)dx+(8x+x^3y)dy=0$$ I have to find this integrating factor. I have arrived to ...
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### Determining integrating factor

Consider $$2x^2y\ln(y)+(x^3+x)y'=0$$ I want to determine the integrating factor $m(x,y)$ of the form $m(x,y)=m(xy)$. Let $a(x,y):=2x^2y\ln(y)$ and $b(x)=x^3+x$. So I want to find $m(x,y)$ such ...
I'm stuck in trying to solve the following ODE: $$y'' + 4xy' + (2+4x^2)y = 0$$ I tried finding an integration factor as if it was exact but I have not succeed. I also tried by trying to get rid of ...