Obtain The Differential Equation By Eliminating Arbitrary Constants ...

English0Maharashtra State BoardHSC Commerce (English Medium) 12th Standard Board ExamQuestion PapersQuestion Papers281Textbook Solutions12313MCQ Online Mock Tests99Important Solutions6742Concept Notes & Videos301Time Tables31SyllabusObtain the differential equation by eliminating arbitrary constants from the following equations. y = (c1 + c2 x) ex - Mathematics and Statistics

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Question

Obtain the differential equation by eliminating arbitrary constants from the following equations.

y = (c1 + c2 x) ex

Sum

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SolutionShow Solution

y = (c1 + c2 x) ex

∴ ye -x = c1 + c2x

Differentiating w.r.t. x, we get

`y (-e^-x) + e ^-x dy/dx = 0 + c_2`

∴`e^-x(dy/dx - y) = c_2`

Again, differentiating w.r.t. x, we get

`e^-x((d^2y)/dx^2-dy/dx) - e^-x(dy/dx-y) = 0`

∴`e^-x((d^2y)/dx^2-dy/dx - dy/dx+ y) = 0`

∴`(d^2y)/dx^2 - 2dy/dx + y = 0`

shaalaa.comFormation of Differential Equation by Eliminating Arbitary Constant Report Error Is there an error in this question or solution?Q 1.3Q 1.2Q 1.4Chapter 8: Differential Equation and Applications - Exercise 8.2 [Page 163]

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Balbharati Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State BoardChapter 8 Differential Equation and ApplicationsExercise 8.2 | Q 1.3 | Page 163

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