Solve y 10y 21y 40y 100y 0 given that y xe5x is a solut

Solve y\'\'\'\' 10y\'\'\' + 21y\'\' + 40y\' 100y = 0 , given that y = xe^(5x) is a solution.

Given that

y\'\'\'\' 10y\'\'\' + 21y\'\' + 40y\' 100y = 0

then the characteristic equation is r⁴ - 10r³ + 21r² + 40r - 100 = 0

Therefore the roots are r = - 2 , 2 , 5 , 5

Then the genaral solution is

y( x ) = C₁ e^-2x + C₂ e^2x + C₃ e^5x + C₄ xe^-5x

^Where C₁, C₂ ,C₃ , and C₄ are arbitrary constants

$Solve y\'\'\'\' 10y\'\'\' + 21y\'\' + 40y\' 100y = 0 , given that y = xe^(5x) is a solution.SolutionGiven that y\'\'\'\' 10y\'\'\' + 21y\'\' + 40y\' 100y = 0 th$

Solve y 10y 21y 40y 100y 0 given that y xe5x is a solut

Solution

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