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Differential Equations

Short Answer Type

131. Solve 4 e^x tan y dx + 3(1 + e^x) sec²y dy = 0.

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Long Answer Type

132.

For the following differential equation, find the general solution:
sec² x tan y dx – sec² y tan x dy = 0.

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Short Answer Type

133.

For the following differential equation, find the general solution:
sec² x tan y dx + sec² y tan x dy = 0.

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134.

Solve:
3e^x tan y dx + (1 – e^x) sec²y dy = 0.

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135.

Solve:
e^x tan y dx + (1 – e^x) sec² y dy = 0.

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136.
Solve:
tan y dx + sec² y tan x dy = 0.

The given differential equation is
tan y dx + sec² y tan x dy = 0 or sec² y tan x dy = - tan y dx
Separating the variables, we get,

fraction numerator sec squared straight y over denominator tan space straight y end fraction dy space equals space minus fraction numerator 1 over denominator tan space straight x end fraction dx

Integrating,

integral fraction numerator sec squared straight y over denominator tan space straight y end fraction dy space equals negative fraction numerator 1 over denominator tan space straight x end fraction dx

therefore space space log space open vertical bar tan space straight y close vertical bar space equals space minus log space open vertical bar sin space straight x close vertical bar space plus space log space straight c apostrophe therefore space space log space open vertical bar tan space straight y close vertical bar space plus space log space open vertical bar sin space straight x close vertical bar space equals space log space straight c apostrophe therefore space space log space open vertical bar tan space straight y space sinx space close vertical bar space equals space log space straight c apostrophe therefore space space open vertical bar tany space sinx close vertical bar space equals space straight c apostrophe therefore space space tany space sinx space space equals space straight A comma space where space straight A space is space constant. space

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137.

Solve:
$left parenthesis 1 plus straight y squared right parenthesis thin space left parenthesis 1 plus log space straight x right parenthesis space dx space plus space straight x space dy space equals space 0$

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138.

Solve:
$left parenthesis 1 plus straight e to the power of 2 straight x end exponent right parenthesis space dy space plus space left parenthesis 1 plus straight y squared right parenthesis space straight e to the power of straight x space dx space equals space 0$

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139.

Solve:
$log dy over dx equals ax plus by.$

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140.

Solve:
$straight x squared left parenthesis straight y minus 1 right parenthesis space dx space plus space straight y squared space left parenthesis straight x minus 1 right parenthesis space dy space equals space 0$

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

Long Answer Type

Short Answer Type

136. Solve:tan y dx + sec2 y tan x dy = 0.

136.
Solve:
tan y dx + sec² y tan x dy = 0.