202301091401

Type :Note Tags : Differential Equations

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Solving a linear differential equations

$$\varphi \left(x,y,y^{\prime }\dots y^{(n)}\right)$$

And

$$y^{(n)}=\Psi \left(x,y,y^{\prime }\dots y^{(n-1)}\right)$$

First Order Differential Equations

Case 1 $y^{\prime }=g(x)$

By Fundamental Theorem of Calculus: $g(x)$ is continuous on $[a,b]$ and $(a,c)\to f(x)=c+\underset{a}{\overset{x}{\int }}g(t)dt$

Case 2

A] Homogenous $y^{\prime }=-p(x)y$

Case

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Related Problems

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References

Solution of a differential equation