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# Find the particular solution of the differential equation $dxdy =−4xy_{2}$ given that $y=1$, when $x=0$.

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## Text solutionVerified

Solution

If $y=0$, the given differential equation can be written as

$y_{2}dy =−4xdx$ $...(1)$

Integrating both sides of equation (1), we get

$∫y_{2}dy =−4∫xdx$

$−y1 =−2x_{2}+C$

$y=2x_{2}−C1 $.....(2)

Substituting $y=1$ and $x=0$ in equation (2), we get, $C=−1$.

Now substituting the value of $C$ in equation (2),

we get the particular solution of the given differential equation as $y=2x_{2}+11 $.

If $y=0$, the given differential equation can be written as

$y_{2}dy =−4xdx$ $...(1)$

Integrating both sides of equation (1), we get

$∫y_{2}dy =−4∫xdx$

$−y1 =−2x_{2}+C$

$y=2x_{2}−C1 $.....(2)

Substituting $y=1$ and $x=0$ in equation (2), we get, $C=−1$.

Now substituting the value of $C$ in equation (2),

we get the particular solution of the given differential equation as $y=2x_{2}+11 $.

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**LIVE**classesQuestion Text | Find the particular solution of the differential equation $dxdy =−4xy_{2}$ given that $y=1$, when $x=0$. |

Updated On | Apr 21, 2023 |

Topic | Differential Equations |

Subject | Mathematics |

Class | Class 12 |

Answer Type | Text solution:1 Video solution: 5 |

Upvotes | 667 |

Avg. Video Duration | 10 min |