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ELEN [110]
3 years ago
9

Rupees500 for 3years at 5 percent?​

Mathematics
1 answer:
Naya [18.7K]3 years ago
6 0

What's the question?

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Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).
Firdavs [7]

Answer:

A) Particular solution:

2x+\frac{1}{2}e^{-x}-\frac{8}{5}

B) Homogeneous solution:

y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))

C) The most general solution is

y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}

Step-by-step explanation:

Given non homogeneous ODE is

y''+4y'+5y=10x+e^{-x}---(1)

To find homogeneous solution:

D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)

To find particular solution:

y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\

Substituting y_{p},y'_{p},y''_{p} in (1)

y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\

Equating the coefficients

5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\

The general solution is

y=y_{h}+y_{p}

from (2) ad (3)

y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}

6 0
2 years ago
Solve by factorization<br> 2x^2 + 3x -20 = 0
saul85 [17]

Answer:

x=2.5 or x=-4

Step-by-step explanation:

factorisation= factors:1, 2, 4, 5, 10, 20 (only the positive factors)

We will use the factors 4 and 5.

=(2x-5)(x+4)=0

2x-5=0   || x+4=0

2x=+5      || x=-4

x=2.5  or x=-4

4 0
2 years ago
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The answer are not in the right order first to answer i will name brainly
Nady [450]

Answer:

it would go pink, purple, green

Step-by-step explanation:

4 0
3 years ago
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Who is good at math I really need help
const2013 [10]
Me I am very good at math I am a tutor
6 0
3 years ago
Which graph best represents the equation x+2y=4
RUDIKE [14]
You didn’t show a picture of the graph, although the equation would be y=-1/2x+2
so every two x spaces forward you should go down one y space and the y should start at 2 when x = 0
3 0
3 years ago
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