TS EAMCET · Maths · Differential Equations
The differential equation for which \(y=a x^2+b x+c\) is the general solution is
- A \(\frac{d^4 y}{d x^4}=0\)
- B \(\frac{d^3 y}{d x^3}=0\)
- C \(\frac{d^5 y}{d x^5}=0\)
- D \(\frac{d^3 y}{d x^3}+\frac{d^4 y}{d x^4}=0\)
Answer & Solution
Correct Answer
(B) \(\frac{d^3 y}{d x^3}=0\)
Step-by-step Solution
Detailed explanation
We have, \(y=a x^2+b x+c\) Here, Number of arbitrary constants are three as \(a, b\) and \(c\) On differentiating both sides w.r.t.' \(x^{\prime} \frac{d y}{d x}=2 a x+b\) Again, \(\frac{d^2 y}{d x^2}=2 a\) Again, differentiate, w.r.t. ' \(x\) ' \(\frac{d^3 y}{d x^3}=0\)
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