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Popular Calculus >

(D^2+2)^3(D^2-3)^2y=0

Solution

(D^{2} + 2)^{3} (D^{2} - 3)^{2} y = 0

Solution

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + c_{3} e^{3 x} + c_{4} x e^{3 x} + c_{5} cos (2 x) + c_{6} sin (2 x) + x (c_{7} cos (2 x) + c_{8} sin (2 x)) + x^{2} (c_{9} cos (2 x) + c_{10} sin (2 x))

Solution steps

(D^{2} + 2)^{3} (D^{2} - 3)^{2} y = 0

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + c_{3} e^{3 x} + c_{4} x e^{3 x} + c_{5} cos (2 x) + c_{6} sin (2 x) + x (c_{7} cos (2 x) + c_{8} sin (2 x)) + x^{2} (c_{9} cos (2 x) + c_{10} sin (2 x))

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + c_{3} e^{3 x} + c_{4} x e^{3 x} + c_{5} cos (2 x) + c_{6} sin (2 x) + x (c_{7} cos (2 x) + c_{8} sin (2 x)) + x^{2} (c_{9} cos (2 x) + c_{10} sin (2 x))

Graph

Popular Examples

y^{''}-y^'-12y=0,y(0)=1,y^'(0)=-2

y^{'''}+7y^{''}+15y^'+9y=0

(d^3y)/(dx^3)-3(d^2y)/(dx^2)+4y=0

Frequently Asked Questions (FAQ)

What is the solution for (D^2+2)^3(D^2-3)^2y=0 ?
The solution for (D^2+2)^3(D^2-3)^2y=0 is