A) \[{{y}_{2}}+{{y}_{1}}+2y=0\]
B) \[{{y}_{2}}-{{y}_{1}}+2y=0\]
C) \[{{y}_{2}}+{{y}_{1}}=0\]
D) \[{{y}_{2}}-{{y}_{1}}-2y=0\]
E) \[{{y}_{2}}-2{{y}_{1}}-y=0\]
Correct Answer: D
Solution :
Given that, \[y=2{{e}^{2x}}-{{e}^{-x}}\] On differentiating w.r.t.\[x,\]we get \[{{y}_{1}}=4{{e}^{2x}}+{{e}^{-x}}\] Now, on again differentiating w.r.t.\[x,\]we get \[{{y}_{2}}=8{{e}^{2x}}-{{e}^{-x}}\] Now, \[{{y}_{2}}-{{y}_{1}}-2y\] \[=8{{e}^{2x}}-{{e}^{-x}}-4{{e}^{2x}}-{{e}^{-x}}-4{{e}^{2x}}+2{{e}^{-x}}\] \[=0\]
You need to login to perform this action.
You will be redirected in
3 sec
