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Class 12-science NCERT Solutions Maths Chapter 9 - Differential Equations

Differential Equations Exercise Ex. 9.1

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Differential Equations Exercise Ex. 9.2

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Differential Equations Exercise Ex. 9.3

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Differential Equations Exercise Ex. 9.4

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Let x and y be the x-coordinate and y-coordinate of the point on the curve respectively.

We know that the slope of a tangent to the curve in the coordinate axes is given by the relation,

 

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Differential Equations Exercise Ex. 9.5

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Differential Equations Exercise Ex. 9.6

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Differential Equations Exercise Misc. Ex.

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begin mathsize 14px style left parenthesis straight i right parenthesis space
x y equals a e to the power of x plus b e to the power of negative x end exponent plus x squared
Differentiating space both space sides space straight w. straight r. straight t space x space we space get
fraction numerator d left parenthesis x y right parenthesis over denominator d x end fraction equals a fraction numerator d over denominator d x end fraction open parentheses e to the power of x close parentheses plus b fraction numerator d over denominator d x end fraction open parentheses e to the power of negative x end exponent close parentheses plus fraction numerator d over denominator d x end fraction left parenthesis 2 x right parenthesis
rightwards double arrow x fraction numerator d y over denominator d x end fraction plus y equals a e to the power of x minus b e to the power of negative x end exponent plus 2 x
Again comma space differentiating space both space the space sides space straight w. straight r. straight t. space x comma space we space get
x fraction numerator d squared y over denominator d x squared end fraction plus fraction numerator d y over denominator d x end fraction plus fraction numerator d y over denominator d x end fraction equals a fraction numerator d over denominator d x end fraction left parenthesis e to the power of x right parenthesis minus b fraction numerator d over denominator d x end fraction left parenthesis e to the power of negative x end exponent right parenthesis plus 2 fraction numerator d over denominator d x end fraction left parenthesis x right parenthesis
rightwards double arrow x fraction numerator d squared y over denominator d x squared end fraction plus 2 fraction numerator d y over denominator d x end fraction equals a e to the power of x plus b e to the power of negative x end exponent plus 2
rightwards double arrow x fraction numerator d squared y over denominator d x squared end fraction plus 2 fraction numerator d y over denominator d x end fraction equals x y minus x squared plus 2
rightwards double arrow x fraction numerator d squared y over denominator d x squared end fraction plus 2 fraction numerator d y over denominator d x end fraction minus x y plus x squared minus 2 equals 0
Hence comma space the space given space function space is space straight a space solution space of space the space corresponding space differential space equation. end style

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