Transformation to linear form by substituting $$v = {y^{1 - n}}$$ of the equation $${{dy} \over {dt}} + p\left( t \right)y = q\left( t \right){y^n},\,\,n > 0$$ will be

$${{dv} \over {dt}} + \left( {1 - n} \right)pv = \left( {1 - n} \right)q$$

$${{dv} \over {dt}} + \left( {1 + n} \right)pv = \left( {1 + n} \right)q$$

$${{dv} \over {dt}} + \left( {1 + n} \right)pv = \left( {1 - n} \right)q$$

$${{dv} \over {dt}} + \left( {1 - n} \right)pv = \left( {1 + n} \right)q$$

GATE 2005 Civil Engineering PYQ — Engineering Mathematics

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Engineering Mathematics · Differential Equations (CE)

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Differential Equations (CE) has appeared in GATE Civil Engineering 63 times across 26 years (2017, 2022, 2023, 2024, 2025, ...).

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