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Vector Algebra

Question
CBSEENMA12032946
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Form a differential equation from the equation y = 2(x2 - 1) + ce-x2.

Solution

The given equation is
y = 2 (x2 - 1) + c e-x2 or yex2 = 2 (x21) ex2 + c
Differentiating both sides w.r.t. x, we get.
                     straight y. straight e to the power of straight x squared end exponent. space 2 space straight x space plus space straight e to the power of straight x squared end exponent. space dy over dx space equals space 2 left parenthesis straight x squared minus 1 right parenthesis space straight e to the power of straight x squared end exponent. space 2 space straight x space plus space 2 straight e to the power of straight x squared end exponent. space space 2 straight x space plus space 0
or          2 xy plus dy over dx space equals space 4 straight x left parenthesis straight x squared minus 1 right parenthesis space plus space 4 straight x space space space space space or space space space dy over dx space equals space 4 straight x left parenthesis straight x squared minus 1 right parenthesis space plus space 4 straight x space minus space 2 xy
which is required differential equation. 

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

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