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Popular Calculus >

2y^{''}+12y=6tan(3x)

Solution

2 y^{^{''}} + 12 y = 6 tan (3 x)

Solution

y = c_{1} cos (6 x) + c_{2} sin (6 x) + cos (6 x) \cdot \int - \frac{6 sin ( 6 x ) tan ( 3 x )}{2} d x + sin (6 x) \cdot \int \frac{6 cos ( 6 x ) tan ( 3 x )}{2} d x

Solution steps

2 y^{''} (x) + 12 y = 6 tan (3 x)

Solve linear ODE:

y = c_{1} cos (6 x) + c_{2} sin (6 x) + cos (6 x) \cdot \int - \frac{6 sin ( 6 x ) tan ( 3 x )}{2} d x + sin (6 x) \cdot \int \frac{6 cos ( 6 x ) tan ( 3 x )}{2} d x

y = c_{1} cos (6 x) + c_{2} sin (6 x) + cos (6 x) \cdot \int - \frac{6 sin ( 6 x ) tan ( 3 x )}{2} d x + sin (6 x) \cdot \int \frac{6 cos ( 6 x ) tan ( 3 x )}{2} d x

Popular Examples

y^{''}+4y^'+5y=-5x+3e^{(-x)}

y^{''}-3y^'+2y=11e^3x,y^1(0)=ex

y^{''}+4y=8x^2+7x

y^{''}+3y=cos(sqrt(3)x)

Frequently Asked Questions (FAQ)

What is the solution for 2y^{''}+12y=6tan(3x) ?
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