What is the solution for f^{''}(x)=acos(2x)+bsin(2x) ?

The solution for f^{''}(x)=acos(2x)+bsin(2x) is f(x)=-(acos(2x))/4-(bsin(2x))/4+c_{1}x+c_{2}

f^{''}(x)=acos(2x)+bsin(2x)

f^{^{''}} (x) = a cos (2 x) + b sin (2 x)

f (x) = - \frac{a cos ( 2 x )}{4} - \frac{b sin ( 2 x )}{4} + c_{1} x + c_{2}

Solution steps

f^{''} (x) = a cos (2 x) + b sin (2 x)

Solve

f^{''} (x) = a cos (2 x) + b sin (2 x) : f^{'} (x) = a \frac{1}{2} sin (2 x) - \frac{1}{2} b cos (2 x) + c_{1}

Solve

f^{'} (x) = a \frac{1}{2} sin (2 x) - \frac{1}{2} b cos (2 x) + c_{1} : f (x) = - \frac{a cos ( 2 x )}{4} - \frac{b sin ( 2 x )}{4} + c_{1} x + c_{2}

f (x) = - \frac{a cos ( 2 x )}{4} - \frac{b sin ( 2 x )}{4} + c_{1} x + c_{2}

n = 1 \sum \infty 3 (\frac{1}{4})^{n - 1}

\int \frac{( x ^{3} )}{( 1 + x ^{2} )} d x

d er i v a t i v e f (- x) = \frac{x}{x ^{2} + 1}

\int \frac{1}{x ^{2} - 361} d x

x \to 0 lim (\frac{x}{- 3 x ^{3} + 2})

What is the solution for f^{''}(x)=acos(2x)+bsin(2x) ?
The solution for f^{''}(x)=acos(2x)+bsin(2x) is f(x)=-(acos(2x))/4-(bsin(2x))/4+c_{1}x+c_{2}