Q.1 (vi) y=c²+c/x is solution of ____. A. x⁴(dy/dx)²-xdy/dx-y=0 B. x²(dy/dx)²+y=0 C. x³(d²y/dx²)-xdy/dx+y=0 D. xd²y/dx²=4y

Answer: A. x⁴(dy/dx)²-xdy/dx-y=0 Answer: (a) x⁴(dy/dx)²-xdy/dx-y=0 Differentiating, dy/dx=-c/x² , so c=-x²dy/dx . Substituting in y=c²+c/x : y=x⁴(dy/dx)²-xdy/dx , i.e. x⁴(dy/dx)²-xdy/dx-y=0 .

Chapter: Differential Equations· Mathematics & Statistics Part 2

\(y=c^2+\dfrac{c}{x}\) is solution of ____.

Q.1 (vi) \(y=c^2+\dfrac{c}{x}\) is solution of ____.

A. \(x^4\left(\dfrac{dy}{dx}\right)^2-x\dfrac{dy}{dx}-y=0\)

B. \(x^2\left(\dfrac{dy}{dx}\right)^2+y=0\)

C. \(x^3\left(\dfrac{d^2y}{dx^2}\right)-x\dfrac{dy}{dx}+y=0\)

D. \(x\dfrac{d^2y}{dx^2}=4y\)

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Answer: A. \(x^4\left(\dfrac{dy}{dx}\right)^2-x\dfrac{dy}{dx}-y=0\)

Answer: (a) \(x^4\left(\dfrac{dy}{dx}\right)^2-x\dfrac{dy}{dx}-y=0\)

Differentiating, \(\dfrac{dy}{dx}=-\dfrac{c}{x^2}\), so \(c=-x^2\dfrac{dy}{dx}\).

Substituting in \(y=c^2+\dfrac cx\): \(y=x^4\left(\dfrac{dy}{dx}\right)^2-x\dfrac{dy}{dx}\), i.e. \(x^4\left(\dfrac{dy}{dx}\right)^2-x\dfrac{dy}{dx}-y=0\).

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