Find the solution of the differential equation that satisfies the given initial condition. dy/dx = xe^y, y(0) = 0

1 answer:

3 0

$\dfrac{\mathrm dy}{\mathrm dx}=xe^y$
$e^{-y}\,\mathrm dy=x\,\mathrm dx$
$-e^{-y}=\dfrac{x^2}2+C$

$y(0)=0$
$\implies-1=C$
$\implies -e^{-y}=\dfrac{x^2}2-1$
$e^{-y}=1-\dfrac{x^2}2$
$-y=\ln\left(1-\dfrac{x^2}2\right)$
$y=-\ln\left(1-\dfrac{x^2}2\right)$

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What is the missing step in this proof? a. ∠abc ≅ ∠dbe b. ∠bca ≅ ∠bde c. ∠acb ≅ ∠deb d. ∠bde ≅ ∠ade e. ∠cab ≅ ∠dac

Nana76 [90]

Based on the reflexive property of congruency, the missing step in the proof is: A. ∠ABC ≅ ∠DBE

<h3>What is the Reflexive Property of Congruency?</h3>

The reflexive property of congruency states that an angle will always be congruent to itself.

In the diagram given, we can prove that ∠ABC ≅ ∠DBE based on the reflexive property.

Therefore, the missing step in nthe proof is: A. ∠ABC ≅ ∠DBE

Learn more about reflexive property on:

brainly.com/question/1601404

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