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Fynjy0 [20]
3 years ago
8

Soles the differential equations using the substitution u=y’; u’=y” y’y”=2

Mathematics
1 answer:
GarryVolchara [31]3 years ago
3 0

Answer with explanation:

The given differential equation

  y'y''=2--------(1)

We have to apply the following substitution

  u=y'

 u'=y"

Applying these substitution in equation (1)

u u'=2

u \frac{du}{dx}=2\\\\ u du=2 dx\\\\ \int u du=\int 2 dx\\\\\frac{u^2}{2}=2 x+K\\\\\frac{y'^2}{2}=2 x+K\\\\y'^2=4 x+2 K\\\\y'=(4 x+2 K)^{\frac{1}{2}}\\\\ dy=(4 x+2 K)^{\frac{1}{2}} d x\\\\\int dy=\int(4 x+2 K)^{\frac{1}{2}} d x\\\\y=\frac{(4 x+2 K)^{\frac{3}{2}}}{4 \times \frac{3}{2}}+J\\\\y=\frac{(4 x+2 K)^{\frac{3}{2}}}{6}+J

Where , J and K are constant of Integration.

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Answer:

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Step-by-step explanation:

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so total is 12+x grams

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6 0
2 years ago
This question that I need to help on is Unknown angle problems (with Algebra)​
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6 0
3 years ago
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What is the relationship between the lines with the following equations? 2x+8y=16 y=4x+7
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6 0
3 years ago
The Bowen family's pancake recipe uses 2 teaspoons of baking powder for every
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5 0
3 years ago
Can 24 7ths be equal to another fraction or be simplified in another way
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3 years ago
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