AP EAMCET · Maths · Differential Equations
Which one of the following is a homogeneous differential equation?
- A \(\frac{d y}{d x}=x^3+(\sin x) y\)
- B \(\frac{d y}{d x}=\left(x^3+y^3\right) e^{\frac{x}{y}}+x \sqrt{y}\)
- C \(\left(x^2+y^2\right) d x=2 x y d y\)
- D \(x \frac{d y}{d x}=y+e^{\frac{x}{y}}\)
Answer & Solution
Correct Answer
(C) \(\left(x^2+y^2\right) d x=2 x y d y\)
Step-by-step Solution
Detailed explanation
\(\because\) Degree of each term in the differential equation \(\left(x^2+y^2\right) d x=2 x y\) dy is same (equal to 2 ). \(\therefore\left(x^2+y^2\right) \mathrm{dx}=2 x y d y\) is a homogeneous differential equation.
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