Solve $straight x to the power of 5 dy over dx space equals space minus straight y to the power of 5$

Solution

The given differential equation is
$straight x to the power of 5 dy over dx equals negative straight y to the power of 5 space space space space or space space space space space dy over dx space equals space minus straight y to the power of 5 over straight x to the power of 5$
Separating the variables, we get,
$1 over straight y to the power of 5 dy space equals space minus 1 over straight x to the power of 5 dx$
Integrating, $integral 1 over straight y to the power of 5 dy space equals space minus integral 1 over straight x to the power of 5 dx space space or space space space integral straight y to the power of negative 5 end exponent dy space equals negative integral straight x to the power of negative 5 end exponent dx$
$therefore space space space space space space fraction numerator straight y to the power of negative 4 end exponent over denominator negative 4 end fraction space equals space minus fraction numerator straight x to the power of negative 4 end exponent over denominator negative 4 end fraction plus straight c apostrophe space space space space space or space space space fraction numerator 1 over denominator negative 4 straight y to the power of 4 end fraction space equals space fraction numerator 1 over denominator 4 straight x to the power of 4 end fraction plus straight c apostrophe$
or $1 over straight x to the power of 4 plus 1 over straight y to the power of 4 space equals space minus 4 straight c apostrophe$
or $straight x to the power of negative 4 end exponent plus straight y to the power of negative 4 end exponent space equals space straight c comma space space where space straight c space equals space minus 4 straight c apostrophe.$

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Vector Algebra

Solve $straight x to the power of 5 dy over dx space equals space minus straight y to the power of 5$

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:
y' + y = e^x

Determine order and degree (if defined) of differential equations:
y'' + (y')² + 2 y = 0

Determine order and degree (if defined) of differential equations:
y″ + 2y′ + sin y = 0

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Vector Algebra

Solve

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:y' + y = ex

Determine order and degree (if defined) of differential equations:y'' + (y')2 + 2 y = 0

Determine order and degree (if defined) of differential equations:y″ + 2y′ + sin y = 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Solve $straight x to the power of 5 dy over dx space equals space minus straight y to the power of 5$

Determine order and degree (if defined) of differential equations:
y' + y = e^x

Determine order and degree (if defined) of differential equations:
y'' + (y')² + 2 y = 0

Determine order and degree (if defined) of differential equations:
y″ + 2y′ + sin y = 0