AP EAMCET · Maths · Differential Equations
The substitution \(x=v y\) converts which one of the following differential equation to an equation solvabie by variable separable method?
- A \(\left(y^2-2 x^2 y\right) d x=\left(x^2-2 x y^2\right) d y\)
- B \(x^2 d y-y d x=\sqrt{x^2+y^2} d x\)
- C \(\frac{d y}{d x}=\frac{y^2}{x+\sqrt{x y}}\)
- D \(\left(1+2 e^{\frac{x}{y}}\right)+2 e^{\frac{x}{y}}\left(1-\frac{x}{y}\right) \frac{d y}{d x}=0\)
Answer & Solution
Correct Answer
(D) \(\left(1+2 e^{\frac{x}{y}}\right)+2 e^{\frac{x}{y}}\left(1-\frac{x}{y}\right) \frac{d y}{d x}=0\)
Step-by-step Solution
Detailed explanation
\(x=v y\) converts those differential equation to variable separable form which we have Homogenous function \(f(x, y)=\frac{d y}{d x}\) of order zero ie each term should have equal power. \(\therefore\) Option (a) \& (b) are not homogeneous. Hence they are incorrect option.…
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