Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
We have,
\[5\frac{dy}{dx} = e^x y^4 \]
\[ \Rightarrow \frac{5}{y^4}dy = e^x dx\]
Integrating both sides, we get
\[\int\frac{5}{y^4}dy = \int e^x dx\]
\[ \Rightarrow \frac{- 5}{3 y^3} = e^x + C\]
\[\text{ Hence, }\frac{- 5}{3 y^3} = e^x +\text{ C is the required solution .}\]
APPEARS IN
संबंधित प्रश्न
Assume that a rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop.
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.
Verify that y2 = 4a (x + a) is a solution of the differential equations
\[y\left\{ 1 - \left( \frac{dy}{dx} \right)^2 \right\} = 2x\frac{dy}{dx}\]
Verify that \[y = e^{m \cos^{- 1} x}\] satisfies the differential equation \[\left( 1 - x^2 \right)\frac{d^2 y}{d x^2} - x\frac{dy}{dx} - m^2 y = 0\]
(1 + x) (1 + y2) dx + (1 + y) (1 + x2) dy = 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).
x2 dy + y (x + y) dx = 0
(x + 2y) dx − (2x − y) dy = 0
Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{xy}{x^2 + y^2}\] given that y = 1 when x = 0.
Solve the following initial value problem:-
\[x\frac{dy}{dx} - y = \left( x + 1 \right) e^{- x} , y\left( 1 \right) = 0\]
If the marginal cost of manufacturing a certain item is given by C' (x) = \[\frac{dC}{dx}\] = 2 + 0.15 x. Find the total cost function C (x), given that C (0) = 100.
The slope of the tangent at a point P (x, y) on a curve is \[\frac{- x}{y}\]. If the curve passes through the point (3, −4), find the equation of the curve.
Find the curve for which the intercept cut-off by a tangent on x-axis is equal to four times the ordinate of the point of contact.
Radium decomposes at a rate proportional to the quantity of radium present. It is found that in 25 years, approximately 1.1% of a certain quantity of radium has decomposed. Determine approximately how long it will take for one-half of the original amount of radium to decompose?
The differential equation of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = C\] is
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
y = ex + 1 y'' − y' = 0
Form the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constant.
Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
For the following differential equation find the particular solution.
`dy/ dx = (4x + y + 1),
when y = 1, x = 0
Solve the following differential equation.
`dy/dx + y = e ^-x`
Solve the following differential equation.
`dy/dx + y` = 3
Choose the correct alternative.
The differential equation of y = `k_1 + k_2/x` is
Solve:
(x + y) dy = a2 dx
Solve the differential equation `("d"y)/("d"x) + y` = e−x
Choose the correct alternative:
General solution of `y - x ("d"y)/("d"x)` = 0 is
The solution of differential equation `x^2 ("d"^2y)/("d"x^2)` = 1 is ______
Solve the following differential equation
`y log y ("d"x)/("d"y) + x` = log y
Solution of `x("d"y)/("d"x) = y + x tan y/x` is `sin(y/x)` = cx
`d/(dx)(tan^-1 (sqrt(1 + x^2) - 1)/x)` is equal to:
