🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning Numerade Educator ### Problem 5 Medium Difficulty # Which of the following functions are solutions of the differential equation$ y^{"} + y = \sin x ? $(a)$ y = \sin x $(b)$ y = \cos x $(c)$ y = \frac {1}{2} x \sin x $(d)$ y = - \frac{1}{2} x \cos x $### Answer ##$\mathrm{LHS}=y^{\prime \prime}+y=-\frac{1}{2}(-x \cos x-2 \sin x)+\left(-\frac{1}{2} x \cos x\right)=\sin x=\mathrm{RHS},$so$y=-\frac{1}{2} x \cos x\$ is a solution of the differential equation.

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Differential Equations

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