Question

Solve
$dy over dx space equals space fraction numerator xe to the power of straight x logx plus straight e to the power of straight x over denominator straight x space cosy end fraction$

Solution

The given differential equation is $dy over dx equals fraction numerator xe to the power of straight x logx plus straight e to the power of straight x over denominator straight x space cosy end fraction$
Separating the variables, we get,
$cosy space dy space equals space fraction numerator xe to the power of straight x logx plus straight e to the power of straight x over denominator straight x end fraction dx space space or space space cosy space dy space equals space straight e to the power of straight x open parentheses fraction numerator straight x space logx space plus space 1 over denominator straight x end fraction close parentheses dx$
or $cosy space dy space equals space straight e to the power of straight x open parentheses logx plus 1 over straight x close parentheses dx space space space rightwards double arrow space space integral space cosy space dy space equals space integral straight e to the power of straight x open parentheses logx plus 1 over straight x close parentheses dx$
$therefore space space space sin space straight y space equals space straight e to the power of straight x space logx space plus space straight c space space space space space space space space space open square brackets because space space integral straight e to the power of straight x open curly brackets straight f left parenthesis straight x right parenthesis plus straight f apostrophe left parenthesis straight x right parenthesis close curly brackets dx space equals space straight e to the power of straight x space straight f left parenthesis straight x right parenthesis space plus space straight c close square brackets$
which is required solution.

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Vector Algebra

Solve
$dy over dx space equals space fraction numerator xe to the power of straight x logx plus straight e to the power of straight x over denominator straight x space cosy end fraction$

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Solve
$dy over dx space equals space fraction numerator xe to the power of straight x logx plus straight e to the power of straight x over denominator straight x space cosy end fraction$

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