AP EAMCET · Maths · Differential Equations
The general solution of the differential equation \((1+\tan y)(d y-d x)+2 x d y=0\) is
- A \(e^{\mathrm{x}}(y \cos x+\sin x)+\sin x=c\)
- B \(e^{\mathrm{x}}(y \cos x+\mathrm{y} \sin x-\sin x)+\cos x=0\)
- C \(e^y(x \cos y+x \sin y-\sin y)=c\)
- D \(e^y(x \cos y+x \sin y+\sin y)=c\)
Answer & Solution
Correct Answer
(C) \(e^y(x \cos y+x \sin y-\sin y)=c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & (1+\tan y)(d x-d y)+2 x d y=0 \\ & \Rightarrow \frac{d x}{d y}+\frac{2 x}{1+\tan y}=1 \\ & \text { I.F. }=e^{\int \frac{2}{1+\tan y} d y}=e^{y+\log (\sin y+\cos y)} \\ & =e^y(\sin y+\cos y) \end{aligned}\) Solution is…
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