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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Popular Examples

y^{''}+40y^'+400y=100sin(10t)

y^{''}-y^'-6y=14cos(3x)

y^{''}+4000y^'+4000000y=36

(d^2y)/(dx^2)+14(dy)/(dx)+49y=4e^{5x}

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+3y=cos(sqrt(3x)) ?
The solution for y^{''}+3y=cos(sqrt(3x)) is