MCQ
The general solution of differential equation is $(y+c)^2=c x$ where ccis an arbitrary constant. The order and degree of the differential equation are respectively:
- ✓$1, 2$
- B$2, 2$
- C$1, 1$
- D$2, 1$
✓
Answer
Correct option: A.
$1, 2$
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 $2$
$=(\text{y}+\text{c})^2=\text{cx}$
$\Rightarrow\text{y}=\sqrt{\text{cx}}-\text{c}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\sqrt{\text{c}}}{\text{x}}$
$\Rightarrow\Big(\frac{\text{dy}}{\text{dx}}\Big)^2=\frac{\text{c}}{\text{x}}$
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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