Advertisements
Advertisements
Question
Find the differential equation whose general solution is
x3 + y3 = 35ax.
Advertisements
Solution
x3 + y3 = 35ax ...(i)
Differentiating w.r.t. x, we get
`3x^3 + 3y^3 dy/dx = 35a` ...(ii)
Substituting (ii) in (i), we get
`x^3 + y^3 = (3x^2 + 3y^2 dy/dx)x`
∴ `x^3 + y^3 = 3x^3 + 3x*y^2 dy/dx`
∴ `2x^3 - y^3 +3xy^2dy/dx =0`, which is the required differential equation.
RELATED QUESTIONS
Solve the equation for x: `sin^(-1) 5/x + sin^(-1) 12/x = π/2, x ≠ 0`
Find the differential equation of all the parabolas with latus rectum '4a' and whose axes are parallel to x-axis.
Show that the function y = A cos x + B sin x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + y = 0\]
Show that y = ex (A cos x + B sin x) is the solution of the differential equation \[\frac{d^2 y}{d x^2} - 2\frac{dy}{dx} + 2y = 0\]
Verify that y = log \[\left( x + \sqrt{x^2 + a^2} \right)^2\] satisfies the differential equation \[\left( a^2 + x^2 \right)\frac{d^2 y}{d x^2} + x\frac{dy}{dx} = 0\]
In a bank principal increases at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e0.5 = 1.648).
(x + 2y) dx − (2x − y) dy = 0
Solve the following initial value problem:-
\[\frac{dy}{dx} + y\cot x = 2\cos x, y\left( \frac{\pi}{2} \right) = 0\]
Find the equation of the curve passing through the point \[\left( 1, \frac{\pi}{4} \right)\] and tangent at any point of which makes an angle tan−1 \[\left( \frac{y}{x} - \cos^2 \frac{y}{x} \right)\] with x-axis.
Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y + 2 (x + 1) = 2e2x.
Find the equation of the curve passing through the point (0, 1) if the slope of the tangent to the curve at each of its point is equal to the sum of the abscissa and the product of the abscissa and the ordinate of the point.
Write the differential equation obtained eliminating the arbitrary constant C in the equation xy = C2.
The differential equation obtained on eliminating A and B from y = A cos ωt + B sin ωt, is
What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?
If xmyn = (x + y)m+n, prove that \[\frac{dy}{dx} = \frac{y}{x} .\]
Solve the following differential equation.
`dy/dx + 2xy = x`
Solve the differential equation:
`e^(dy/dx) = x`
Solve the differential equation sec2y tan x dy + sec2x tan y dx = 0
Choose the correct alternative:
Solution of the equation `x("d"y)/("d"x)` = y log y is
Given that `"dy"/"dx" = "e"^-2x` and y = 0 when x = 5. Find the value of x when y = 3.
Solve the differential equation `dy/dx + xy = xy^2` and find the particular solution when y = 4, x = 1.
