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Which of the following differential equations has y = c1 ex + c2 e-x as the general solution? $(A)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}+y=0(B)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}-y=0(C)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}+1=0(D)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}-1=0$.
Which of the following differential equations has y = c1 ex + c2 e-x as the general solution? $(A)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}+y=0(B)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}-y=0(C)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}+1=0(D)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}-1=0$.
CBSE | Class 12 | Differential Equations | Exercise 9.3 | NCERT
Which of the following differential equations has y = c1 ex + c2 e-x as the general solution? $(A)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}+y=0(B)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}-y=0(C)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}+1=0(D)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}-1=0$.

  

   [From eq. (i)]

 

Therefore,The correct option is option (B) .

i

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