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If    \dpi{100} \frac{dy}{dx}=y+3> 0\; and\; y(0)=2,then\; y(1n\: 2)  is equal to

  • Option 1)

    13

  • Option 2)

    – 2

  • Option 3)

    7

  • Option 4)

    5

 

Answers (1)

best_answer

As we learnt in 

Solution of Differential Equation -

\frac{\mathrm{d}y }{\mathrm{d} x} =f\left ( ax+by+c \right )

put

 Z =ax+by+c

 

 

- wherein

Equation with convert to

\int \frac{dz}{bf\left ( z \right )+a} =x+c

 

 

 

\frac{dy}{dx}=y+3>0,\:\:y(0)=2,\:\:y(ln2)=?

\Rightarrow \int \frac{dy}{y+3}= \int dx

\Rightarrow \log \left| y+3 \right|=x+C

\Rightarrow \log 5=C

\Rightarrow \log \left| y+3 \right|=x+ \log 5

=\log 2+ \log 5=\log 10

y+3=10\:\:\:\:\:\:\Rightarrow y=7

 

 


Option 1)

13

This option is incorrect.

Option 2)

– 2

This option is incorrect.

Option 3)

7

This option is correct.

Option 4)

5

This option is incorrect.

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