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Popular Calculus >

y^{''}+2y=-sec(x)

Solution

y^{^{''}} + 2 y = - sec (x)

Solution

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

Solution steps

y^{''} (x) + 2 y = - sec (x)

Solve linear ODE:

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

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

Popular Examples

y^{''}+y=\H(t)-\H(t-pi/2)

y^{''}+4y^'+5y=25x^2+13sin(2x)

y^{''}+2y^'-3y=4e^{-3x}+10sin(x)

y^{''''}+2y^{''}+y=9t+10

y^{'''}-2y^{''}+y^'=e^xcos(2x)

Frequently Asked Questions (FAQ)

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