Is $y = \cos x + C _ { 1 } x + C _ { 2 }$ the general solution to the differential equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } = \cos x$ ?

Question

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The general solution to the differential equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } = \cos x$ should include the particular solution to $\cos x$ and the general solution to the homogeneous equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } = 0$, which is $C_1 x + C_2$. The particular solution to $\cos x$ is $-\cos x$, so the general solution is $y = -\cos x + C_1 x + C_2$.

Is y=cos⁡x+C1x+C2y = \cos x + C _ { 1 } x + C _ { 2 }y=cosx+C1​x+C2​

Is $y = \cos x + C _ { 1 } x + C _ { 2 }$