If d x d y = y + 3 > 0 and y ( 0 ) = 2 , then y ( ln 2 ) is equal to

d x d y = y + 3 ⇒ y + 3 d y = d x ln ( y + 3 ) = x + c x = 0 ⇒ y = 2 ⇒ ln 5 = 0 + c c = ln 5 ln ( y + 3 ) = x + ln 5 y + 3 = e x + l n 5 ⇒ y + 3 = e l n 2 + l n 5 y + 3 = 10 ⇒ y = 7

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Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationVariable separableEasy2 minPYQ_2011

MathematicsEasynumerical range

If $\frac{d y}{d x} = y + 3 > 0$ and $y (0) = 2$ , then $y (ln 2)$ is equal to

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Solution:

$\frac{d y}{d x} = y + 3 \Rightarrow \frac{d y}{y + 3} = d x$ $ln (y + 3) = x + c$ $x = 0 \Rightarrow y = 2$ $\Rightarrow ln 5 = 0 + c$ $c = ln 5$ $ln (y + 3) = x + ln 5$ $y + 3 = e^{x + l n 5} \Rightarrow y + 3 = e^{l n 2 + l n 5}$ $y + 3 = 10 \Rightarrow y = 7$

Stream:JEESubject:MathematicsTopic:Differential EquationSubtopic:Variable separable

⏱ 2mℹ️ Source: PYQ_2011

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