Question

Which of the following statement(s) are true for the given differential equation? x^2y" - 5xy' + 13y = 30x^2 L?tfen bir ya da daha fazlas?n? se?in: r^2 - 5r + 13 = 0 is a characteristic polynomial of the differential equation. Its homogeneous solution is y_H = e^{3z}(C_1 cos(2x) + C_2 sin(2x)) for arbitrary constants C_1 and C_2. It is a second order nonhomogeneous Cauchy-Euler differential equation. To find particular solution, the variation of parameters can be used. Its characteristic polynomial has 3 + 2i and 3 - 2i complex roots. Using t = ln x, we get d^2y/dt^2 - 6dy/dt + 13y = 30e^{2t}.

          Which of the following statement(s) are true for the given differential equation?
x^2y" - 5xy' + 13y = 30x^2
L?tfen bir ya da daha fazlas?n? se?in:
r^2 - 5r + 13 = 0 is a characteristic polynomial of the differential equation.
Its homogeneous solution is y_H = e^{3z}(C_1 cos(2x) + C_2 sin(2x)) for arbitrary constants C_1 and C_2.
It is a second order nonhomogeneous Cauchy-Euler differential equation.
To find particular solution, the variation of parameters can be used.
Its characteristic polynomial has 3 + 2i and 3 - 2i complex roots.
Using t = ln x, we get d^2y/dt^2 - 6dy/dt + 13y = 30e^{2t}.

Which of the following statement(s) are true for the given differential equation?
x^2y" - 5xy' + 13y = 30x^2
L?tfen bir ya da daha fazlas?n? se?in:
r^2 - 5r + 13 = 0 is a characteristic polynomial of the differential equation.
Its homogeneous solution is yH = e^3z(C1 cos(2x) + C2 sin(2x)) for arbitrary constants C1 and C2.
It is a second order nonhomogeneous Cauchy-Euler differential equation.
To find particular solution, the variation of parameters can be used.
Its characteristic polynomial has 3 + 2i and 3 - 2i complex roots.
Using t = ln x, we get d^2y/dt^2 - 6dy/dt + 13y = 30e^2t.

Added by Roy C.

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