GATE 2026 MT – Question 46
The solution of $10x^2\frac{d^2y}{dx^2}-20x\frac{dy}{dx}+22.4y=0$ is $y=c_1x^{m_1}+c_2x^{m_2}$, where $m_1\ne m_2$. The value of $m_1+m_2$ is ________. (Answer in integer.)
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Correct answer: 3 to 3
Explanation
Substitute $y=x^m$ into the Euler equation to obtain $10m(m-1)-20m+22.4=0$, or $10m^2-30m+22.4=0$.
By the sum-of-roots relation, $m_1+m_2=-(-30)/10=$ **3**.