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(X3 − 2y3) Dx + 3x2 Y Dy = 0 - Mathematics

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प्रश्न

(x3 − 2y3) dx + 3x2 y dy = 0

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उत्तर

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अध्याय 22: Differential Equations - Revision Exercise [पृष्ठ १४६]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 22 Differential Equations
Revision Exercise | Q 48 | पृष्ठ १४६

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

The differential equation of `y=c/x+c^2` is :

(a)`x^4(dy/dx)^2-xdy/dx=y`

(b)`(d^2y)/dx^2+xdy/dx+y=0`

(c)`x^3(dy/dx)^2+xdy/dx=y`

(d)`(d^2y)/dx^2+dy/dx-y=0`


Solve : 3ex tanydx + (1 +ex) sec2 ydy = 0

Also, find the particular solution when x = 0 and y = π.


If y = P eax + Q ebx, show that

`(d^y)/(dx^2)=(a+b)dy/dx+aby=0`


Find the particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 0.


Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

y = Ax : xy′ = y (x ≠ 0)


Write the order of the differential equation associated with the primitive y = C1 + C2 ex + C3 e−2x + C4, where C1, C2, C3, C4 are arbitrary constants.


The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is


The solution of the differential equation \[\frac{dy}{dx} = 1 + x + y^2 + x y^2 , y\left( 0 \right) = 0\] is


Solution of the differential equation \[\frac{dy}{dx} + \frac{y}{x}=\sin x\] is


If m and n are the order and degree of the differential equation \[\left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\], then


The solution of the differential equation \[\frac{dy}{dx} + 1 = e^{x + y}\], is


The solution of x2 + y \[\frac{dy}{dx}\]= 4, is


The solution of the differential equation (x2 + 1) \[\frac{dy}{dx}\] + (y2 + 1) = 0, is


Find the general solution of the differential equation \[x \cos \left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x .\]


Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{x\left( 2 \log x + 1 \right)}{\sin y + y \cos y}\] given that

\[y = \frac{\pi}{2}\] when x = 1.

`(2ax+x^2)(dy)/(dx)=a^2+2ax`


\[\frac{dy}{dx} + 2y = \sin 3x\]


`(dy)/(dx)+ y tan x = x^n cos x, n ne− 1`


For the following differential equation, find the general solution:- `y log y dx − x dy = 0`


For the following differential equation, find the general solution:- \[\frac{dy}{dx} + y = 1\]


For the following differential equation, find a particular solution satisfying the given condition:

\[x\left( x^2 - 1 \right)\frac{dy}{dx} = 1, y = 0\text{ when }x = 2\]


Solve the following differential equation:-

\[x\frac{dy}{dx} + 2y = x^2 \log x\]


Solve the following differential equation:-

\[\left( x + 3 y^2 \right)\frac{dy}{dx} = y\]


The solution of the differential equation `x "dt"/"dx" + 2y` = x2 is ______.


The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______.


y = x is a particular solution of the differential equation `("d"^2y)/("d"x^2) - x^2 "dy"/"dx" + xy` = x.


If y = e–x (Acosx + Bsinx), then y is a solution of ______.


Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.


The general solution of ex cosy dx – ex siny dy = 0 is ______.


Which of the following is the general solution of `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + y` = 0?


The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.


General solution of `("d"y)/("d"x) + y` = sinx is ______.


Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.

The value of c in the particular solution given that y(0) = 0 and k = 0.049 is ______.


The member of arbitrary constants in the particulars solution of a differential equation of third order as


Which of the following differential equations has `y = x` as one of its particular solution?


Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.


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