Advertisements
Advertisements
प्रश्न
Solve: `("d"y)/("d"x) + "e"^x + y"e"^x = 0`
Advertisements
उत्तर
`("d"y)/("d"x) + "e"^x + y"e"^x = 0`
`("d"y)/("d"x) = - y"e"^x - "e"^x`
`("d"y)/("d"x) = - "e"^x (y + 1)`
`1/((y + 1)) "d"y = - "e"^x "d"x`
Integrating on both sides
`int 1/((y + 1)) "d"x = - int "e"^x "d"x`
⇒ log (y + 1) = `- "e"^x + "c"`
APPEARS IN
संबंधित प्रश्न
Solve the following differential equation:
`("d"y)/("d"x) = "e"^(x + y) - x^3"e"^y`
Solve the following differential equation:
`[x + y cos(y/x)] "d"x = x cos(y/x) "d"y`
Solve the following differential equation:
`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`
Solve: ydx – xdy = 0 dy
Solve the following homogeneous differential equation:
`(x - y) ("d"y)/("d"x) = x + 3y`
Solve the following homogeneous differential equation:
`x ("d"y)/("d"x) - y = sqrt(x^2 + y^2)`
Solve the following homogeneous differential equation:
`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`
Solve the following homogeneous differential equation:
The slope of the tangent to a curve at any point (x, y) on it is given by (y3 – 2yx2) dx + (2xy2 – x3) dy = 0 and the curve passes through (1, 2). Find the equation of the curve
Solve the following:
`x ("d"y)/("d"x) + 2y = x^4`
Choose the correct alternative:
If y = ex + c – c3 then its differential equation is
