a) -(-(+1))=1))))))))))))))))
![xy'-y=x^2\cos x\\ \\ x \frac{dy}{dx} -y-x^2\cos x=0\\ \\ xdy+(-y-x^2\cos x)dx=0](https://tex.z-dn.net/?f=xy%27-y%3Dx%5E2%5Ccos+x%5C%5C+%5C%5C+x+%5Cfrac%7Bdy%7D%7Bdx%7D+-y-x%5E2%5Ccos+x%3D0%5C%5C+%5C%5C+xdy%2B%28-y-x%5E2%5Ccos+x%29dx%3D0)
![\displaystyle \frac{\partial M}{\partial x} = \frac{\partial x}{\partial x} =1\\ \\ \\ \frac{\partial N}{\partial y}= \frac{\partial(-y-x^2\cos x)}{\partial y} =-1](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cfrac%7B%5Cpartial+M%7D%7B%5Cpartial+x%7D+%3D+%5Cfrac%7B%5Cpartial+x%7D%7B%5Cpartial+x%7D+%3D1%5C%5C+%5C%5C+%5C%5C++%5Cfrac%7B%5Cpartial+N%7D%7B%5Cpartial+y%7D%3D+%5Cfrac%7B%5Cpartial%28-y-x%5E2%5Ccos+x%29%7D%7B%5Cpartial+y%7D+%3D-1+)
Поскольку
![\displaystyle \frac{\partial M}{\partial x}\ne \frac{\partial N}{\partial y}](https://tex.z-dn.net/?f=%5Cdisplaystyle++%5Cfrac%7B%5Cpartial+M%7D%7B%5Cpartial+x%7D%5Cne+%5Cfrac%7B%5Cpartial+N%7D%7B%5Cpartial+y%7D++)
, то дифференциальное уравнение не является в полных дифференциалах
Найдем для него интегрирующий множитель
![\displaystyle \phi(x)= \frac{ \frac{\partial N}{\partial y}- \frac{\partial M}{\partial x} }{M} = \frac{-1-1}{x} \\ \\ \\ \nu(x)=e^\big{\int- \frac{2}{x}dx }= \frac{1}{x^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cphi%28x%29%3D+%5Cfrac%7B+%5Cfrac%7B%5Cpartial+N%7D%7B%5Cpartial+y%7D-+%5Cfrac%7B%5Cpartial+M%7D%7B%5Cpartial+x%7D++%7D%7BM%7D+%3D+%5Cfrac%7B-1-1%7D%7Bx%7D+%5C%5C+%5C%5C+%5C%5C+%5Cnu%28x%29%3De%5E%5Cbig%7B%5Cint-+%5Cfrac%7B2%7D%7Bx%7Ddx+%7D%3D+%5Cfrac%7B1%7D%7Bx%5E2%7D+)
Умножим обе части уравнения на
![\dfrac{1}{x^2}](https://tex.z-dn.net/?f=+%5Cdfrac%7B1%7D%7Bx%5E2%7D+)
, получаем
![\displaystyle \frac{dy}{dx} \cdot \frac{1}{x} - \frac{y}{x^2} =\cos x\\ \\ \\ \frac{dy}{dx}\cdot \frac{1}{x} +y\cdot \frac{d( \frac{1}{x}) }{dx} =\cos x\\ \\ \\ \frac{d}{dx}\bigg( \frac{y}{x}\bigg)=\cos x](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cfrac%7Bdy%7D%7Bdx%7D+%5Ccdot+%5Cfrac%7B1%7D%7Bx%7D+-+%5Cfrac%7By%7D%7Bx%5E2%7D+%3D%5Ccos+x%5C%5C+%5C%5C+%5C%5C++%5Cfrac%7Bdy%7D%7Bdx%7D%5Ccdot+%5Cfrac%7B1%7D%7Bx%7D+%2By%5Ccdot+%5Cfrac%7Bd%28+%5Cfrac%7B1%7D%7Bx%7D%29+%7D%7Bdx%7D++%3D%5Ccos+x%5C%5C+%5C%5C+%5C%5C++%5Cfrac%7Bd%7D%7Bdx%7D%5Cbigg%28+%5Cfrac%7By%7D%7Bx%7D%5Cbigg%29%3D%5Ccos+x++)
Интегрируя обе части уравнения, получаем:
![\displaystyle \frac{y}{x} =\int\limits {\cos x} \, dx \\ \\ \\ \frac{y}{x} =\sin x+C\\ \\ \\ \boxed{y=x(\sin x+C)}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cfrac%7By%7D%7Bx%7D++%3D%5Cint%5Climits+%7B%5Ccos+x%7D+%5C%2C+dx+%5C%5C+%5C%5C+%5C%5C+%5Cfrac%7By%7D%7Bx%7D+%3D%5Csin+x%2BC%5C%5C+%5C%5C+%5C%5C+%5Cboxed%7By%3Dx%28%5Csin+x%2BC%29%7D)
21+30+31+8+365+365=820 дней осталось до 2018 года и 8 июня.
Б)
9x+4-4(5x+1)=9x+4-20x-4=-11x=-11*1=-11
в)
3(3x-2)-(6x-2)=9x-6-6x+2=3x-4=3*(-2)-4=-6-4=-10
г)
-5(3x-1)+2(5x+1)=-15x+5+10x+2=-5x+7=-5*3+7=-15+7=-8
д)
5(3x+2)-3(5x+3)=15x+10-15x-9=1
е)
-8(3x-6)+4(6x-12)=-24x+48+24x-48=0