= 0 – (x2 × 1) + (x × x)
= -x2 + x2
= 0
Which of the following differential equations has y = x as one of its particular solution? $(A)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}-{{x}^{2}}\frac{dy}{dx}+xy=x(B)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}+{{x}^{{}}}\frac{dy}{dx}+xy=x(C)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}-{{x}^{2}}\frac{dy}{dx}+xy=0(D)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}+{{x}^{{}}}\frac{dy}{dx}+xy=0$
Which of the following differential equations has y = x as one of its particular solution? $(A)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}-{{x}^{2}}\frac{dy}{dx}+xy=x(B)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}+{{x}^{{}}}\frac{dy}{dx}+xy=x(C)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}-{{x}^{2}}\frac{dy}{dx}+xy=0(D)\frac{{{\partial }^{2}}y}{\partial {{x}^{2}}}+{{x}^{{}}}\frac{dy}{dx}+xy=0$