F(X)=4SINX-5COSX
f'(X)=4COSX+5SINX
<span>36:9=4
27:9=9
</span><span>3×8=24
4</span><span>×8=32</span>
<span>(X-7)-(2х+9)= -13
х-7-2х-9=-13
-х-16=-13
-х=-13+16
-х=3
<u>х=-3</u>
</span>14-(3+Х)=16
14-3-х=16
11-х=16
х=11-16
<u>х=-5</u>
<span>2х-(Х+4)=20</span>
2х-х-4=20
х-4=20
х=20+4
<u>х=24</u>
Теперь находим производную от общего решения:
![y'=[(C_1sinx+C_2cosx)e^{2x}]'=(C_1sinx+C_2cosx)'*e^{2x}+ \\ \\ +(e^{2x})'*(C_1sinx+C_2cosx)=(C_1cosx-C_2sinx)*e^{2x}+2e^{2x}* \\ \\ *(C_1sinx+C_2cosx)](https://tex.z-dn.net/?f=y%27%3D%5B%28C_1sinx%2BC_2cosx%29e%5E%7B2x%7D%5D%27%3D%28C_1sinx%2BC_2cosx%29%27%2Ae%5E%7B2x%7D%2B+%5C%5C+%5C%5C+%2B%28e%5E%7B2x%7D%29%27%2A%28C_1sinx%2BC_2cosx%29%3D%28C_1cosx-C_2sinx%29%2Ae%5E%7B2x%7D%2B2e%5E%7B2x%7D%2A+%5C%5C+%5C%5C+%2A%28C_1sinx%2BC_2cosx%29)
составляем систему с общим решением и его производной:
![\left\{\begin{matrix} y=(C_1sinx+C_2cosx)e^{2x} \\ y'=(C_1cosx-C_2sinx)*e^{2x}+2e^{2x}* (C_1sinx+C_2cosx) \end{matrix}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D+y%3D%28C_1sinx%2BC_2cosx%29e%5E%7B2x%7D+%5C%5C+y%27%3D%28C_1cosx-C_2sinx%29%2Ae%5E%7B2x%7D%2B2e%5E%7B2x%7D%2A+%28C_1sinx%2BC_2cosx%29+%5Cend%7Bmatrix%7D%5Cright.)
Подставляем x=0, <span>y=1, y'=-1
</span>
![\left\{\begin{matrix} 1=(C_1sin0+C_2cos0)e^{2*0} \\ -1=(C_1cos0-C_2sin0)*e^{2*0}+2e^{2*0}* (C_1sin0+C_2cos0) \end{matrix}\right. \\ \\ \left\{\begin{matrix} 1=C_2 \\ -1=C_1+2C_2 \end{matrix}\right. \\ \\ -1=C_1+2 \\ \\ C_1=-3 \\ C_2=1 \\ \\ \\ OTBET: \ y=(cosx-3sinx)e^{2x}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D+1%3D%28C_1sin0%2BC_2cos0%29e%5E%7B2%2A0%7D+%5C%5C+-1%3D%28C_1cos0-C_2sin0%29%2Ae%5E%7B2%2A0%7D%2B2e%5E%7B2%2A0%7D%2A+%28C_1sin0%2BC_2cos0%29+%5Cend%7Bmatrix%7D%5Cright.+%5C%5C++%5C%5C+%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D+1%3DC_2+%5C%5C+-1%3DC_1%2B2C_2+%5Cend%7Bmatrix%7D%5Cright.+%5C%5C++%5C%5C++-1%3DC_1%2B2+%5C%5C+%5C%5C+C_1%3D-3+%5C%5C+C_2%3D1+%5C%5C++%5C%5C++%5C%5C+OTBET%3A+%5C+y%3D%28cosx-3sinx%29e%5E%7B2x%7D)
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