WBJEE · Maths · Differential Equations
If \(y^{\prime \prime}-3 y^{\prime}+2 y=0\) where \(y(0)=1, y^{\prime}(0)=0\), then the value of \(y\) at \(x=\log , 2\) is
- A 1
- B -1
- C 2
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Hints: } \frac{d^2 y}{d x^2}-3 \frac{d y}{d x}+2 y=0 \\ & m^2-3 m+2=0, \quad y=A e^x+B e^{2 x} \\ & m=1, m=2, y^1=A e^x+2 B e^{2 x} \\ & y=0, A+B=1 \quad A+2 B=0, A=2, B=-1 \\ & y=2 e^x-e^{2 x} \\ & y=0 \quad \text { at } x=\ell n 2 \end{aligned} \]
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