WBJEE · Maths · Differential Equations
If \(u(x)\) and \(v(x)\) are two independent solutions of the differential equation \(\frac{d^{2} y}{d x^{2}}+b \frac{d y}{d x}+c y=0\) then additional solution(s) of the given differential equation is(are)
- A \(y=5 u(x)+8 v(x)\)
- B \(y=c_{1}\{u(x)-v(x)\}+c_{2} v(x), c_{1}\) and \(c_{2}\) are arbitrary constants
- C \(y=c_{1}u(x) v(x)+c_{2} u(x) / v(x) . \quad c_{1}\) and \(c_{2}\) are arbitrary constants
- D \(y=u(x) \vee(x)\)
Answer & Solution
Correct Answer
(B) \(y=c_{1}\{u(x)-v(x)\}+c_{2} v(x), c_{1}\) and \(c_{2}\) are arbitrary constants
Step-by-step Solution
Detailed explanation
We know that \(u(x)\) and \(v(x)\) are two independent solutions of the given differential equation, then their linear combination is also the solution of the given equation. Here, we see that \(y=5 u(x)+8 v(x)\) is a linear combination and \(y=c_{1}\{u(x)-v(x)\}+c_{2} v(x)\) is…
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