Найти общее решение данного уравнения и частное решение, удовлетворяющее данным начальным условиям.
Приложения:
![](https://st.uroker.com/files/4d6/4d6dbaa74f16923681c1e54e51165a32.jpg)
SRT1905:
какого именно уравнения?
Ответы
Ответ дал:
1
7)
![xy'+2y= \frac{1}{x} xy'+2y= \frac{1}{x}](https://tex.z-dn.net/?f=xy%27%2B2y%3D+%5Cfrac%7B1%7D%7Bx%7D+)
![y'+ \frac{2y}{x} = \frac{1}{x^2} y'+ \frac{2y}{x} = \frac{1}{x^2}](https://tex.z-dn.net/?f=y%27%2B+%5Cfrac%7B2y%7D%7Bx%7D+%3D+%5Cfrac%7B1%7D%7Bx%5E2%7D+)
![y=uv y=uv](https://tex.z-dn.net/?f=y%3Duv)
![u'v+uv'+ \frac{2uv}{x} = \frac{1}{x^2} u'v+uv'+ \frac{2uv}{x} = \frac{1}{x^2}](https://tex.z-dn.net/?f=u%27v%2Buv%27%2B+%5Cfrac%7B2uv%7D%7Bx%7D+%3D+%5Cfrac%7B1%7D%7Bx%5E2%7D)
![u'v+u(v'+ \frac{2v}{x} )= \frac{1}{x^2} u'v+u(v'+ \frac{2v}{x} )= \frac{1}{x^2}](https://tex.z-dn.net/?f=u%27v%2Bu%28v%27%2B+%5Cfrac%7B2v%7D%7Bx%7D+%29%3D+%5Cfrac%7B1%7D%7Bx%5E2%7D)
![v'+ \frac{2v}{x}=0 v'+ \frac{2v}{x}=0](https://tex.z-dn.net/?f=v%27%2B+%5Cfrac%7B2v%7D%7Bx%7D%3D0)
![\frac{dv}{dx}=- \frac{2v}{x} \frac{dv}{dx}=- \frac{2v}{x}](https://tex.z-dn.net/?f=+%5Cfrac%7Bdv%7D%7Bdx%7D%3D-+%5Cfrac%7B2v%7D%7Bx%7D)
![\frac{dv}{dx}=- \frac{2v}{x} \frac{dv}{dx}=- \frac{2v}{x}](https://tex.z-dn.net/?f=+%5Cfrac%7Bdv%7D%7Bdx%7D%3D-+%5Cfrac%7B2v%7D%7Bx%7D)
![\int \frac{dv}{v}=-2\int \frac{dx}{x} \int \frac{dv}{v}=-2\int \frac{dx}{x}](https://tex.z-dn.net/?f=%5Cint+%5Cfrac%7Bdv%7D%7Bv%7D%3D-2%5Cint+%5Cfrac%7Bdx%7D%7Bx%7D)
![ln |v| =-2ln|x| ln |v| =-2ln|x|](https://tex.z-dn.net/?f=ln+%7Cv%7C+%3D-2ln%7Cx%7C)
![ln |v| =ln| \frac{1}{x^2} | ln |v| =ln| \frac{1}{x^2} |](https://tex.z-dn.net/?f=ln+%7Cv%7C+%3Dln%7C+%5Cfrac%7B1%7D%7Bx%5E2%7D+%7C)
![v=\frac{1}{x^2} v=\frac{1}{x^2}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B1%7D%7Bx%5E2%7D)
![u'v=\frac{1}{x^2} u'v=\frac{1}{x^2}](https://tex.z-dn.net/?f=u%27v%3D%5Cfrac%7B1%7D%7Bx%5E2%7D)
![\frac{u'}{x^2}=\frac{1}{x^2} \frac{u'}{x^2}=\frac{1}{x^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bu%27%7D%7Bx%5E2%7D%3D%5Cfrac%7B1%7D%7Bx%5E2%7D)
![\frac{du}{dx}=1 \frac{du}{dx}=1](https://tex.z-dn.net/?f=%5Cfrac%7Bdu%7D%7Bdx%7D%3D1)
![\int du =\int dx \int du =\int dx](https://tex.z-dn.net/?f=%5Cint+du+%3D%5Cint+dx)
![u=x+C u=x+C](https://tex.z-dn.net/?f=u%3Dx%2BC)
![y=uv= \frac{x+C}{x^2} y=uv= \frac{x+C}{x^2}](https://tex.z-dn.net/?f=y%3Duv%3D+%5Cfrac%7Bx%2BC%7D%7Bx%5E2%7D+)
![y(3)=\frac{3+C}{3^2} =1 y(3)=\frac{3+C}{3^2} =1](https://tex.z-dn.net/?f=y%283%29%3D%5Cfrac%7B3%2BC%7D%7B3%5E2%7D+%3D1)
![3+C=9 3+C=9](https://tex.z-dn.net/?f=3%2BC%3D9)
![C=6 C=6](https://tex.z-dn.net/?f=C%3D6)
![y=\frac{x+6}{x^2} y=\frac{x+6}{x^2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx%2B6%7D%7Bx%5E2%7D+)
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