हिंदी

Solve the following differential equation. dydx=x2y+y - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Solve the following differential equation.

`dy/dx = x^2 y + y`

योग
Advertisements

उत्तर

`dy/dx = x^2 y + y = (x^2 +1)y`

∴ `1/y dy = (x^2 + 1)dx`

Integrating on both sides, we get

` int 1/y dy  = int (x^2+1) dx`

∴ `log  | y | = x^3/3 + x + c`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Differential Equation and Applications - Exercise 8.3 [पृष्ठ १६५]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 8 Differential Equation and Applications
Exercise 8.3 | Q 1.1 | पृष्ठ १६५

संबंधित प्रश्न

\[\left( \frac{dy}{dx} \right)^2 + \frac{1}{dy/dx} = 2\]

\[\sqrt[3]{\frac{d^2 y}{d x^2}} = \sqrt{\frac{dy}{dx}}\]

Form the differential equation representing the family of ellipses having centre at the origin and foci on x-axis.


Show that the differential equation of which \[y = 2\left( x^2 - 1 \right) + c e^{- x^2}\]  is a solution is \[\frac{dy}{dx} + 2xy = 4 x^3\]


Differential equation \[x\frac{dy}{dx} = 1, y\left( 1 \right) = 0\]

Function y = log x


\[\sin^4 x\frac{dy}{dx} = \cos x\]

\[\left( x^3 + x^2 + x + 1 \right)\frac{dy}{dx} = 2 x^2 + x\]

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

\[\sqrt{1 + x^2} dy + \sqrt{1 + y^2} dx = 0\]

(1 − x2) dy + xy dx = xy2 dx


Solve the following differential equation:
\[\text{ cosec }x \log y \frac{dy}{dx} + x^2 y^2 = 0\]


\[\frac{dr}{dt} = - rt, r\left( 0 \right) = r_0\]

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

Solve the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + \left( 1 + y^2 \right) = 0\], given that y = 1, when x = 0.


The volume of a spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of the balloon after `t` seconds.


In a bank principal increases at the rate of r% per year. Find the value of r if ₹100 double itself in 10 years (loge 2 = 0.6931).


\[\frac{dy}{dx} = \left( x + y + 1 \right)^2\]

\[\frac{dy}{dx}\cos\left( x - y \right) = 1\]

3x2 dy = (3xy + y2) dx


Solve the following initial value problem:-

\[dy = \cos x\left( 2 - y\text{ cosec }x \right)dx\]


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.


Solve the following differential equation : \[y^2 dx + \left( x^2 - xy + y^2 \right)dy = 0\] .


Find the equation of the plane passing through the point (1, -2, 1) and perpendicular to the line joining the points A(3, 2, 1) and B(1, 4, 2). 


Solve the following differential equation.

xdx + 2y dx = 0


Solve the following differential equation.

y dx + (x - y2 ) dy = 0


Solve:

(x + y) dy = a2 dx


Solve the differential equation `("d"y)/("d"x) + y` = e−x 


Solve the following differential equation y2dx + (xy + x2) dy = 0


There are n students in a school. If r % among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×