Maths · Ordinary differential equations, their order and degree
Assertion The order of the differential equation, of which is a solution, is 2 R
Assertion The order of the differential equation, of which \( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{c} \boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{b} \boldsymbol{e}^{-\boldsymbol{x}}+\boldsymbol{x}^{\boldsymbol{2}} \) is a solution, is 2 Reason The differential equation is \( x \frac{d^{2} y}{d x^{2}}+ \) \( 2 \frac{d y}{d x}-x y+x^{2}-2=0 \)
- 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. Both Assertion and Reason are incorrect
Step-by-step solution
The given function has two arbitrary constants, so its differential equation is of order 2. However, substituting the function into the claimed differential equation does not yield an identity, so the reason is incorrect.
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