Verify that $y=a+\dfrac{b}{x}$ is a solution of $x\dfrac{d^2y}{dx^2}+2\dfrac{dy}{dx}=0$.

Verify that y=a+(b)/(x) is a solution of x(d²y)/(dx²)+2(dy)/(dx)=0.

Exercise 6.3 · Q31

y=a+\dfrac{b}{x}

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Differentiate $y=a+\dfrac{b}{x}$ twice: $\dfrac{dy}{dx}=-\dfrac{b}{x^2}$ , $\dfrac{d^2y}{dx^2}=\dfrac{2b}{x^3}$ . Substitute into $x\dfrac{d^2y}{dx^2}+2\dfrac{dy}{dx}$ : $x\cdot\dfrac{2b}{x^3}+2\left(-\dfrac{b}{x^2}\right)=\dfrac{2b}{x^2}-\dfrac{2b}{x^2}=0$ …

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Q.Verify that $y=a+\dfrac{b}{x}$ is a solution of $x\dfrac{d^2y}{dx^2}+2\dfrac{dy}{dx}=0$ .

Concept understanding — General and Particular Solutions of a Differential Equation

Q.Verify that y=a+bxy=a+\dfrac{b}{x}y=a+xb​ is a solution of xd2ydx2+2dydx=0x\dfrac{d^2y}{dx^2}+2\dfrac{dy}{dx}=0xdx2d2y​+2dxdy​=0.

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Q.Verify that $y=a+\dfrac{b}{x}$ is a solution of $x\dfrac{d^2y}{dx^2}+2\dfrac{dy}{dx}=0$ .

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