ExamBro
ExamBro
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

  1. A \(y^{\prime \prime}+4 y^{\prime}+2 y=0\)
  2. B \(y^{\prime \prime}-4 y^{\prime}+2 y=0\)
  3. C \(y^{\prime \prime}-4 y^{\prime}+4 y=0\)
  4. D \(y^{\prime \prime}-2 \sqrt{2} y^{\prime}+2 y=0\)
Verified Solution

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, \(y^{\prime}=e^{2 x}(2 c \cos h \sqrt{2} x+2 d \sin h \sqrt{2} x\) \(+\sqrt{2} c \sin h \sqrt{2} x d \sqrt{2} \cos h \sqrt{2} x)\)…