Question

Assertion :The order of the differential equation whose solution is $y=c_1{e}^{2x+c_2}+c_3{e}^{2x+c_4}$ is 4. Reason: Order of the differential equation is the order of the highest order derivative occurring in the differential equation.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Given $y=c_1{e}^{2x+c_2}+c_3{e}^{2x+c_4}$
$y=(c_1{e}^{c_2}+c_3{e}^{c_4})e^{2x}$
$y=\lambda e^{2x}$ (where $\lambda =c_1{e}^{c_2}+c_3{e}^{c_4}$)
$\Rightarrow$ $\frac{dy}{dx}=2\lambda e^{2x}$ $\Rightarrow$ $\frac{dy}{dx}=2y$
$\Rightarrow$ Order of differential equation is 1,

So Assertion (A) is false but Reason (R) is true.