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Find a general solution of the differential equation y"-(5)^(1/2)y=0?

Find a general solution of the differential equation y"-(5)^(1/2)y=0?

Grade:12

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
7 years ago
The given equation is:
\frac{d^2y}{dx^2}-5^{\frac{1}{2}}y=0
Let’s assume a general solution as:
y=y_0\exp{(kx)}
Therefore, we get:
\left(k^2-5^{\frac{1}{2}}\right)e^{kx}=0
Therefore the general solution is:y=y_0exp^{\left( 5^{\frac{1}{4}}x\right )}

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