Advertisements
Advertisements
प्रश्न
`dy/dx = log x`
उत्तर
`dy/dx = log x`
∴ dy = log x dx
Integrating on both sides, we get
∫ 1 dy =∫ (log x × 1) dx
∴ `y = log x ( int1dx ) – int [ d/dx (logx) int 1dx] `
∴ `y = log x(x) – int (1/x xx x ) dx`
= x log x – ∫ 1dx
∴ y = x log x – x + c
APPEARS IN
संबंधित प्रश्न
Find the differential equation of all the parabolas with latus rectum '4a' and whose axes are parallel to x-axis.
Show that Ax2 + By2 = 1 is a solution of the differential equation x \[\left\{ y\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^2 \right\} = y\frac{dy}{dx}\]
Verify that y = cx + 2c2 is a solution of the differential equation
Verify that y = log \[\left( x + \sqrt{x^2 + a^2} \right)^2\] satisfies the differential equation \[\left( a^2 + x^2 \right)\frac{d^2 y}{d x^2} + x\frac{dy}{dx} = 0\]
Differential equation \[\frac{dy}{dx} + y = 2, y \left( 0 \right) = 3\] Function y = e−x + 2
(x2 − y2) dx − 2xy dy = 0
Find the equation to the curve satisfying x (x + 1) \[\frac{dy}{dx} - y\] = x (x + 1) and passing through (1, 0).
Write the differential equation representing the family of straight lines y = Cx + 5, where C is an arbitrary constant.
The differential equation obtained on eliminating A and B from y = A cos ωt + B sin ωt, is
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
`y=sqrt(a^2-x^2)` `x+y(dy/dx)=0`
Solve the differential equation:
`"x"("dy")/("dx")+"y"=3"x"^2-2`
y dx – x dy + log x dx = 0
Solve the following differential equation y log y = `(log y - x) ("d"y)/("d"x)`
Choose the correct alternative:
Solution of the equation `x("d"y)/("d"x)` = y log y is
Given that `"dy"/"dx"` = yex and x = 0, y = e. Find the value of y when x = 1.
Solve the differential equation `"dy"/"dx"` = 1 + x + y2 + xy2, when y = 0, x = 0.