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DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
Question
The general solution of differential equation is (y + c)2 = cx where ccis an arbitrary constant. The order and degree of the differential equation are respectively:
  1. 1, 2
  2. 2, 2
  3. 1, 1
  4. 2, 1
✓

Answer

  1. 1, 2

Solution:

Given equation is

$=(\text{y}+\text{c})^2=\text{cx}$

$\Rightarrow\text{y}=\sqrt{\text{cx}}-\text{c}$

$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\sqrt{\text{c}}}{\text{x}}$

$\Rightarrow\Big(\frac{\text{dy}}{\text{dx}}\Big)^2=\frac{\text{c}}{\text{x}}$

The order of differential equation is the order of the highest derivative in the equation is 1
The degree of differential equation is the power of the highest order derivative in the equation is 2

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