TS EAMCET · Maths · Differential Equations
The substitution required to reduce the differential equation \(t^2 d x+\left(x^2-t x+t^2\right) d t=0\) to a differential equation which can be solved by variables separable method is
- A \(x=\mathrm{V} t\)
- B \(a x+b t=\mathrm{Z}\)
- C \(\mathrm{V}=t x^2\)
- D \(x=t \mathrm{~V}^2\)
Answer & Solution
Correct Answer
(A) \(x=\mathrm{V} t\)
Step-by-step Solution
Detailed explanation
\(\frac{d x}{d t}=-\frac{x^2-t x+t^2}{t^2}=-\left[\left(\frac{x}{t}\right)^2-\left(\frac{x}{t}\right)+1\right]\) The equation is homogeneous, so the substitution required is \(x=\mathrm{V} t\).
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