Answer:
a.P.I=![\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B11%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%29)
b.G.S=![C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x}](https://tex.z-dn.net/?f=C_1Cos%20%5Csqrt2%20x%2BC_2%20Sin%5Csqrt2%20x%2B%5Cfrac%7B1%7D%7B11%7De%5E%7B3x%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%7D)
Step-by-step explanation:
We are given that a linear differential equation
![y''+2y=e^{3x}+x^3](https://tex.z-dn.net/?f=y%27%27%2B2y%3De%5E%7B3x%7D%2Bx%5E3)
We have to find the particular solution
P.I=![\frac{e^{3x}}{D^2+2}+\frac{x^3}{D^2+2}](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7BD%5E2%2B2%7D%2B%5Cfrac%7Bx%5E3%7D%7BD%5E2%2B2%7D)
P.I=![\frac{e^{3x}}{3^2+2}+\frac{1}{2} x^3(1+\frac{D^2}{2})^{-2}](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B3%5E2%2B2%7D%2B%5Cfrac%7B1%7D%7B2%7D%20x%5E3%281%2B%5Cfrac%7BD%5E2%7D%7B2%7D%29%5E%7B-2%7D)
P.I=![\frac{e^{3x}}{11}+\frac{1-2\frac{D^2}{4}+3\frac{D^4}{16}+...}{2}x^3](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B11%7D%2B%5Cfrac%7B1-2%5Cfrac%7BD%5E2%7D%7B4%7D%2B3%5Cfrac%7BD%5E4%7D%7B16%7D%2B...%7D%7B2%7Dx%5E3)
P.I=
(higher order terms can be neglected
P.I=![\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B11%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%29)
b.Characteristics equation
![D^2+2=0](https://tex.z-dn.net/?f=D%5E2%2B2%3D0)
![D=\pm\sqrt2 i](https://tex.z-dn.net/?f=D%3D%5Cpm%5Csqrt2%20i)
C.F=![C_1cos \sqrt2x+C_2 sin\sqrt2 x](https://tex.z-dn.net/?f=C_1cos%20%5Csqrt2x%2BC_2%20sin%5Csqrt2%20x)
G.S=C.F+P.I
G.S=![C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x)](https://tex.z-dn.net/?f=C_1Cos%20%5Csqrt2%20x%2BC_2%20Sin%5Csqrt2%20x%2B%5Cfrac%7B1%7D%7B11%7De%5E%7B3x%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%29)
Answer:
It should be 1300..........
Answer:
-3
Step-by-step explanation:
y = -3x
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is -3 and the y intercept is 0
Answer:
ummm what is this for tho?
Answer:
![\angle P](https://tex.z-dn.net/?f=%5Cangle%20P)
Step-by-step explanation:
Given
![\triangle PRQ = \triangle TSU = 90^o](https://tex.z-dn.net/?f=%5Ctriangle%20PRQ%20%3D%20%5Ctriangle%20TSU%20%3D%2090%5Eo)
![PR = 12](https://tex.z-dn.net/?f=PR%20%3D%2012)
![SU = 16](https://tex.z-dn.net/?f=SU%20%3D%2016)
<em>See attachment</em>
Required
Which sine of angle is equivalent to ![\frac{4}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B5%7D)
Considering ![\triangle PQR](https://tex.z-dn.net/?f=%5Ctriangle%20PQR)
We have:
--- i.e. opposite/hypotenuse
So, we have:
![\sin(P) = \frac{16}{20}](https://tex.z-dn.net/?f=%5Csin%28P%29%20%3D%20%5Cfrac%7B16%7D%7B20%7D)
Divide by 4
![\sin(P) = \frac{4}{5}](https://tex.z-dn.net/?f=%5Csin%28P%29%20%3D%20%5Cfrac%7B4%7D%7B5%7D)
Hence:
is correct