সমাধান করো :`\frac{d y}{d x}=\frac{2 x-3 y}{3 x-2 y}`

dy/dx = frac{2x+y}{x}

x frac{dy}{dx} = y - xcos^2 frac{y}{x}

Solve dy/dx=frac{3x-4y+2}{4x-5y+3}

Fill in the blanks : The direction ratios of the line frac{2x - 1}{3}=frac{4 - y}{1}=frac{3z + 6}{6} are ……… .

If y=f(x) is a differentiable function, then show that frac( d^2 x}{d y^2 } = (dy/dx)^3 . frac{ d^2 y}{d x^2 }

Let y = y(x) be the solution of the differential equation frac{dy}{dx} = 2x (x y)^3 – x (x y) – 1, y(0) = 1 , Then (frac{1}{sqrt 2} y (frac{1}{sqrt 2}))^2 equals.

frac{dP}{dx} = frac{d}{dx} (x^3) (frac{7-2x}{3})^(4)

If x^y = e^(x-y) , then dy/dx = ............ A) frac{1 + x}{1+ log x} B) frac{log x}{(1+ log x)^2} C) frac{1- log x}{1+ log x} D) frac{1 - x}{1+ log x}

solve the equations: frac{2}{sqrt x} + frac{3}{sqrt y} =2 and frac{4}{sqrt x} - frac{9}{sqrt y} =-1

In each of the following examples verify that the given function is a solution of the corresponding differential equation y=Ae^(2x)+Be^(3x)+Ce^(-x), frac{d^3y}{dx^3}-4 frac{d^2y}{dx^2}+dy/dx+6y=0