Question

2. Solve the following initial value problem * (8 Puan) = 8x2e-2y, y(0) = 1 dx O y = 1 In(4x4 + f2) O y = In(2x - 1) O y = -48x²e-2y O y = In(4x4 – 3) O y = {In(2x' + e?) O none of these O y = In(4x4 + 5) O y = 2x4 + e-2y+2 O y = In (2x + e)

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Answer 1

dy 8 x 3 e 24 dx 24 dy = 8x² 27 873 da dhe » e 2o dy Integrating Jezd dy we get = { 8 x² dx 27 e 2 = 8. te 4 24 e = 4x + 2C Taking logarithm both sides, we get birine In er y m (4x4+2C) * 27 m (4x4+2C) → 1 / 1 m (4x+20) Now, given condition is 70 = 1 i. I = m (20) * In ac = 2 e² [Taking cmti logarithm both sides? + C = že? → 2C = CS Scanned with CamScanner

: y = į m (4x"+2.427) ² m (4x²+62) » y 2 which is the required solution. CS Scanned with CamScanner

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