Find all possible functions with the given derivative.y^{\prime}=5-\frac{2}{x^{2}}y=?

banganX

banganX

Answered question

2021-10-02

Find all possible functions with the given derivative.
y=52x2
y=?

Answer & Explanation

yagombyeR

yagombyeR

Skilled2021-10-03Added 92 answers

Step 1
Rearrange the given ODE to get dy in terms of dx.
y=52x2
dydx=52x2
dy=(52x2)dx
dy=5dx2x2dx
Step 2
Integrate both the sides of equation using the properties of indefinite integrals.
dy=5dx2x2dx
y=5dx2x2dx
y=5x2×(x2+12+1)+C
y=5x2×(x11)+C
y=5x+2x+C
Hence, y=5x+2x+C

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-08Added 2605 answers

Answer is given below (on video)

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