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Popular >

y^{''}+y=12x

Solution

y^{^{''}} + y = 12 x

Solution

y = c_{1} cos (x) + c_{2} sin (x) + 12 x

Solution steps

y^{''} (x) + y = 12 x

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + 12 x

y = c_{1} cos (x) + c_{2} sin (x) + 12 x

Popular Examples

y^{''}+4y=2,e^xy(0)=2,y^'(0)=1

y^{^{''}} + 4 y = 2, e^{x} y (0) = 2, y^{^{'}} (0) = 1

(d^2-d-2)y=10cos(x)

(d^{2} - d - 2) y = 10 cos (x)

y^{''}+4y^'+3y=4,e^3ty(0)=2,y^'(0)=7

y^{^{''}} + 4 y^{^{'}} + 3 y = 4, e^{3} t y (0) = 2, y^{^{'}} (0) = 7

y^{''}-5y^'-6y=6x^2-4x-3

y^{^{''}} - 5 y^{^{'}} - 6 y = 6 x^{2} - 4 x - 3

(d^2+4)y=sin^2(x)

(d^{2} + 4) y = sin^{2} (x)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+y=12x ?
The solution for y^{''}+y=12x is y=c_{1}cos(x)+c_{2}sin(x)+12x