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Questions >> JEEMAIN and NEET >> Mathematics >> Class12 >> Differential Equations

If $x= \sec \theta -\cos \theta$ and $y=\sec^n \theta -\cos ^n \theta$ then $\bigg(\large\frac{dy}{dx}\bigg)^2=$

asked Jan 31, 2014 by meena.p

1 answer

If $x= \cos^{-1} \bigg( \large\frac{1}{\sqrt {1+t^2}}\bigg)$ and $\; y= \sin ^{-1} \bigg( \large\frac{1}{\sqrt {1+t^2}}\bigg)$ then $\large\frac{dy}{dx}$

asked Jan 31, 2014 by meena.p

1 answer

If $x^2+y^2=t-\large\frac{1}{t} ,$ $x^4+y^4 =t^2+\large\frac{1}{t^2}$ then $\large\frac{dy}{dx}$

asked Jan 31, 2014 by meena.p

1 answer

If $\phi (x) =f(x) g(x),$ where $f'(x) g'(x) =c$ and $\large\frac {\phi ''}{\phi} =\frac {f''}{f} +\frac{g''}{g}+\frac{Kc}{fg}$ then value of K.

asked Jan 31, 2014 by meena.p

1 answer

Assertion : For the following equation degree $\large\frac{d^4}{dx^4}$ $+\sin \bigg ( \large\frac{d^2y}{dx^2}\bigg)=0$ Reason : Order of DE is the order of highest differentiate coefficient occurring in the equation

asked Jan 31, 2014 by meena.p

1 answer

Solution of differential equation: $X^2= 1+\large\frac{1}{2} \bigg( \large\frac{x}{y}\bigg)^{-1} \frac{dy}{dx} + \large\frac{\bigg(\Large\frac{x}{y}\bigg)^{-2} \bigg(\Large\frac{dy}{dx}\bigg)^{2}}{4 \times 2 \times 1}+ \large\frac{\bigg(\Large\frac{x}{y}\bigg)^{-3} \bigg(\Large\frac{dy}{dx}\bigg)^{3}}{8 \times 3 \times 2 \times 1}+ \large\frac{\bigg(\Large\frac{x}{y}\bigg)^{-4} \bigg(\Large\frac{dy}{dx}\bigg)^{4}}{16 \times 4 \times 3 \times 2 \times 1}+..........$

asked Jan 31, 2014 by meena.p

1 answer

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