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Popular Calculus >

y^{'''}+4y^'=tan(x)

Solution

y^{^{'''}} + 4 y^{^{'}} = tan (x)

Solution

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) - \frac{1}{4} ln (cos (x)) - \frac{cos ( 2 x ) ( tan ( x ) sin ( 2 x ) + ln ( cos ^{2} ( x ) ) )}{8} - \frac{1}{4} sin (2 x) (x - \frac{1}{2} sin (2 x))

Solution steps

y^{'''} (x) + 4 y^{'} (x) = tan (x)

Solve linear ODE:

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) - \frac{1}{4} ln (cos (x)) - \frac{cos ( 2 x ) ( tan ( x ) sin ( 2 x ) + ln ( cos ^{2} ( x ) ) )}{8} - \frac{1}{4} sin (2 x) (x - \frac{1}{2} sin (2 x))

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) - \frac{1}{4} ln (cos (x)) - \frac{cos ( 2 x ) ( tan ( x ) sin ( 2 x ) + ln ( cos ^{2} ( x ) ) )}{8} - \frac{1}{4} sin (2 x) (x - \frac{1}{2} sin (2 x))

Graph

Popular Examples

y^{''}-10y^'+25y=25x+10

(d^2y)/(dx^2)-(dy)/(dx)=sin(x)-cos(x)

4y^{''}+4y^'+y=2e^{-x}

x^{''}+5x^'+17x=12cos(3t)

Frequently Asked Questions (FAQ)

What is the solution for y^{'''}+4y^'=tan(x) ?
The solution for y^{'''}+4y^'=tan(x) is