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In each of the following examples, verify that the given function is a solution of the corresponding differential equation.
| Solution | D.E. |
| y = ex | `dy/ dx= y` |
Concept: undefined >> undefined
Determine the order and degree of the following differential equations.
| Solution | D.E. |
| y = 1 − logx | `x^2(d^2y)/dx^2 = 1` |
Concept: undefined >> undefined
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Determine the order and degree of the following differential equations.
| Solution | D.E |
| y = aex + be−x | `(d^2y)/dx^2= 1` |
Concept: undefined >> undefined
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` |
Concept: undefined >> undefined
Find the differential equation whose general solution is
x3 + y3 = 35ax.
Concept: undefined >> undefined
Form the differential equation from the relation x2 + 4y2 = 4b2
Concept: undefined >> undefined
Solve the following differential equation.
`dy/dx = x^2 y + y`
Concept: undefined >> undefined
Solve the following differential equation.
`(dθ)/dt = − k (θ − θ_0)`
Concept: undefined >> undefined
Solve the following differential equation.
`y^3 - dy/dx = x dy/dx`
Concept: undefined >> undefined
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
Concept: undefined >> undefined
For the following differential equation find the particular solution.
`(x + 1) dy/dx − 1 = 2e^(−y)`,
when y = 0, x = 1
Concept: undefined >> undefined
For each of the following differential equations find the particular solution.
`y (1 + logx)dx/dy - x log x = 0`,
when x=e, y = e2.
Concept: undefined >> undefined
For the following differential equation find the particular solution.
`dy/ dx = (4x + y + 1),
when y = 1, x = 0
Concept: undefined >> undefined
Solve the following differential equation.
xdx + 2y dx = 0
Concept: undefined >> undefined
Solve the following differential equation.
y2 dx + (xy + x2 ) dy = 0
Concept: undefined >> undefined
Solve the following differential equation.
x2y dx − (x3 + y3) dy = 0
Concept: undefined >> undefined
Solve the following differential equation.
`dy /dx +(x-2 y)/ (2x- y)= 0`
Concept: undefined >> undefined
Solve the following differential equation.
(x2 − y2 ) dx + 2xy dy = 0
Concept: undefined >> undefined
Solve the following differential equation.
`xy dy/dx = x^2 + 2y^2`
Concept: undefined >> undefined
Find the equation of tangent and normal to the curve at the given points on it.
y = 3x2 - x + 1 at (1, 3)
Concept: undefined >> undefined
