WBJEE · Maths · Differential Equations
The differential equation of the family of curves \(y=e^{x}(A \cos x+B \sin x)\) where \(A, B\) are arbitrary constants is
- A \(\frac{d^{2} y}{d x^{2}}-9 x=13\)
- B \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0\)
- C \(\frac{d^{2} y}{d x^{2}}+3 y=4\)
- D \(\left(\frac{d y}{d x}\right)^{2}+\frac{d y}{d x}-x y=0\)
Answer & Solution
Correct Answer
(B) \(\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0\)
Step-by-step Solution
Detailed explanation
Hint: \(y=e^{x}(A \cos x+B \sin x)\) Differentiating w.r.t. x:- \(y^{\prime}=y+e^{x}(-A \sin x+B \cos x)\) Differentiating w.r.t. \(x\) once again:-…
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