AP EAMCET · Maths · Differential Equations
If \(\mathrm{c}\) and \(\mathrm{d}\) are arbitrary constants, then \(y=e^{2 x}(\cosh \sqrt{2} x+d \sinh \sqrt{2} x)\) is the general solution of the differential equation
- A \(y^{\prime \prime}+4 y^{\prime}+2 y=0\)
- B \(y^{\prime \prime}-4 y^{\prime}+2 y=0\)
- C \(y^{\prime \prime}-4 y^{\prime}+4 y=0\)
- D \(y^{\prime \prime}-2 \sqrt{2} y^{\prime}+2 y=0\)
Answer & Solution
Correct Answer
(B) \(y^{\prime \prime}-4 y^{\prime}+2 y=0\)
Step-by-step Solution
Detailed explanation
\(y=e^{2 x}(c \cos h \sqrt{2} x+d \sin h \sqrt{2} x)\) Then, \(y^{\prime}=e^{2 x}(2 c \cos h \sqrt{2} x+2 d \sin h \sqrt{2} x\) \(+\sqrt{2} c \sin h \sqrt{2} x d \sqrt{2} \cos h \sqrt{2} x)\)…
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