$$x^{\prime \prime }=\cos \left(t\right)$$

$$x^{\prime \prime }+x^{\prime }=0$$

$$x^{\prime \prime }+x^{\prime }=0$$

$$x^{\prime \prime }-x^{\prime }=1$$

$$x^{\prime \prime }+x=t$$

$$x^{\prime \prime }+6x^{\prime }=12t+2$$

$$x^{\prime \prime }-2x^{\prime }+2x=2$$

$$x^{\prime \prime }+4x^{\prime }+4x=4$$

$$2x^{\prime \prime }-2x^{\prime }=(t+1){\mathrm{e}}^t$$

$$x^{\prime \prime }+x=2\cos \left(t\right)$$