Advertisements
Advertisements
प्रश्न
Solve the following differential equation.
`dy/dx = x^2 y + y`
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`
APPEARS IN
संबंधित प्रश्न
Prove that:
`int_0^(2a)f(x)dx = int_0^af(x)dx + int_0^af(2a - x)dx`
If 1, `omega` and `omega^2` are the cube roots of unity, prove `(a + b omega + c omega^2)/(c + s omega + b omega^2) = omega^2`
For the following differential equation verify that the accompanying function is a solution:
| Differential equation | Function |
|
\[y = \left( \frac{dy}{dx} \right)^2\]
|
\[y = \frac{1}{4} \left( x \pm a \right)^2\]
|
xy (y + 1) dy = (x2 + 1) dx
Solve the following differential equation:
\[xy\frac{dy}{dx} = 1 + x + y + xy\]
(y2 − 2xy) dx = (x2 − 2xy) dy
2xy dx + (x2 + 2y2) dy = 0
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.
The differential equation obtained on eliminating A and B from y = A cos ωt + B sin ωt, is
Show that y = ae2x + be−x is a solution of the differential equation \[\frac{d^2 y}{d x^2} - \frac{dy}{dx} - 2y = 0\]
The differential equation `y dy/dx + x = 0` represents family of ______.
Choose the correct option from the given alternatives:
The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is
Determine the order and degree of the following differential equations.
| Solution | D.E. |
| ax2 + by2 = 5 | `xy(d^2y)/dx^2+ x(dy/dx)^2 = y dy/dx` |
For each of the following differential equations find the particular solution.
(x − y2 x) dx − (y + x2 y) dy = 0, when x = 2, y = 0
For the following differential equation find the particular solution.
`dy/ dx = (4x + y + 1),
when y = 1, x = 0
Solve the following differential equation.
(x2 − y2 ) dx + 2xy dy = 0
Solve the following differential equation.
`xy dy/dx = x^2 + 2y^2`
Choose the correct alternative.
The differential equation of y = `k_1 + k_2/x` is
Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`
For the differential equation, find the particular solution
`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0
Choose the correct alternative:
Solution of the equation `x("d"y)/("d"x)` = y log y is
A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution
Given that `"dy"/"dx"` = yex and x = 0, y = e. Find the value of y when x = 1.
A man is moving away from a tower 41.6 m high at a rate of 2 m/s. If the eye level of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of 30 m from the foot of the tower, is
