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Question
Verify that y = cx + 2c2 is a solution of the differential equation
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Solution
We have,
\[y = cx + 2 c^2..............(1)\]
Differentiating both sides of (1) with respect to x, we get
Now,
\[2 \left( \frac{dy}{dx} \right)^2 + x\frac{dy}{dx} - y\]
\[ = 2 c^2 + cx - cx - 2 c^2 = 0 ...........\left[\text{Using }\left( 1 \right)\text{ and }\left( 2 \right) \right]\]
\[ \Rightarrow 2 \left( \frac{dy}{dx} \right)^2 + x\frac{dy}{dx} - y = 0\]
Hence, the given function is the solution to the given differential equation.
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