Fizaa A.

asked • 07/09/20

Find the 5th ODE


Given  a 5th order ODE:

LaTeX: a_5 \, y^{(5)} \, + \, a_4 \, y^{(4)} \, + \, a_3 \, y^{\prime \prime \prime} \, + \, a_2 \, y^{\prime \prime} \, + \, a_1 \, y^{\prime} \, + \, a_0 \, y = 0 \qquad \qquad (*)            

if its algebraic (characteristic) equationLaTeX: a_5 \, \lambda^5 + a_4 \, \lambda^4 + a_3 \, \lambda^3 + a_2 \, \lambda^2 + a_1 \, \lambda + a_0 = 0         

has roots as:  LaTeX: 1, 1, 1; \, {\vec i}, {\vec i}       ,

then the general solution of (*) is:

2 Answers By Expert Tutors

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Yefim S. answered • 07/09/20

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General solution y = (C1x2 + C2x + C3)ex + C4sinx + C5cosx.

i and i impossible, it must be i and -i because we dill with ODE with real coefficients.

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Fizaa A.

y^2*dx+ (xy+1) dy=0 is Select a function from below options so that if both sides of the equation are multiplied by the function, then the new ODE is exact. a.) y^(-2) b.) x c.) y^(-1) d.) x/y Please help
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07/09/20

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