JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y = y _1( x )\) and \(y = y _2( x )\) be the solution curves of the differential equation \(\frac{d y}{d x}=y+7\) with initial conditions \(y_1(0)=0, y_2(0)=1\) respectively. Then the curves \(y=y_1(x)\) and \(y=y_2(x)\) intersect at
- A Two points
- B no point
- C infinite number of points
- D one point
Answer & Solution
Correct Answer
(B) no point
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=y+7 \Rightarrow \frac{d y}{d x}-y=7\) \(\text { I.F. }=e^{-x}\) \(ye ^{-x}=\int 7 e ^{- x } dx\) \(\Rightarrow ye ^{- x }=-7 e ^{- x }+ c\) \(\Rightarrow y =-7+c e ^{ x }\) \(-7+7 e ^{ x }=-7+8 e ^{ x }\) \(\Rightarrow e ^{ x }=0\) No solution
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