Advertisements
Advertisements
Question
The solution of `dy/dx + x^2/y^2 = 0` is ______
Options
x3 + y3 = 7
x2 + y2 = c
x3 + y3 = c
x + y = c
Solution
The solution of `dy/dx + x^2/y^2 = 0` is x3 + y3 = c
APPEARS IN
RELATED QUESTIONS
Prove that:
`int_0^(2a)f(x)dx = int_0^af(x)dx + int_0^af(2a - x)dx`
Show that Ax2 + By2 = 1 is a solution of the differential equation x \[\left\{ y\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^2 \right\} = y\frac{dy}{dx}\]
Hence, the given function is the solution to the given differential equation. \[\frac{c - x}{1 + cx}\] is a solution of the differential equation \[(1+x^2)\frac{dy}{dx}+(1+y^2)=0\].
Solve the following initial value problem:-
\[x\frac{dy}{dx} - y = \left( x + 1 \right) e^{- x} , y\left( 1 \right) = 0\]
Find the equation of the curve which passes through the point (1, 2) and the distance between the foot of the ordinate of the point of contact and the point of intersection of the tangent with x-axis is twice the abscissa of the point of contact.
Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.
Solve the differential equation:
`"x"("dy")/("dx")+"y"=3"x"^2-2`
Solve the following differential equation.
xdx + 2y dx = 0
Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0
Choose the correct alternative:
Differential equation of the function c + 4yx = 0 is
Solution of `x("d"y)/("d"x) = y + x tan y/x` is `sin(y/x)` = cx