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JEE Mains · Maths · STD 12 - 9. differential equations
If a curve passes through the origin and the slope of the tangent to it at any point \(( x , y )\) is \(\frac{x^{2}-4 x+y+8}{x-2},\) then this curve also passes through the point
- A \((5,4)\)
- B \((4,5)\)
- C \((4,4)\)
- D \((5,5)\)
Answer & Solution
Correct Answer
(D) \((5,5)\)
Step-by-step Solution
Detailed explanation
Given \(y(0)=0\) \(\& \frac{ dy }{ dx }=\frac{( x -2)^{2}+ y +4}{ x -2}\) \(\Rightarrow \frac{ dy }{ dx }-\frac{ y }{ x -2}=( x -2)+\frac{4}{ x -2}\) \(\Rightarrow I . F .= e ^{-\int \frac{1}{ x -2} dx }=\frac{1}{ x -2}\) Solution of L.D.E.…
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