TS EAMCET · Maths · Differential Equations
Observe the following statements I. If \(d y+2 x y d x=2 e^{-x^2} d x\), then \(y e^{x^2}=2 x+c\) II. If \(y e^{-x^2}-2 x=c\), then \(d x=\left(2 e^{-x^2}-2 x y\right) d y\) which of the following is a correct statement?
- A Both I and II are true
- B Neither I nor II is true
- C I is false, but II is true
- D I is false, II is true
Answer & Solution
Correct Answer
(C) I is false, but II is true
Step-by-step Solution
Detailed explanation
I. \(d y+2 x y d x=2 e^{-x^2} d x\) \(\Rightarrow \quad \frac{d y}{d x}+2 x y=2 e^{-x^2}\) This is a linear differential equation in \(y\) Here, \(P=2 x, Q=2 e^{-x^2}\) \(\therefore \text { I.F. }=e^{\int P d x}=e^{\int 2 x d x}=e^{x^2}\) \(\therefore\) Complete solution is…
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