Active forum topics
- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Eliminate the Arbitrary Constants
- Law of cosines
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Integration of 4x^2/csc^3x√sinxcosx dx
- application of minima and maxima
- Sight Distance of Vertical Parabolic Curve
- Application of Differential Equation: Newton's Law of Cooling
New forum topics
- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Integration of 4x^2/csc^3x√sinxcosx dx
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Newton's Law of Cooling
- Law of cosines
- Can you help me po to solve this?
- Eliminate the Arbitrary Constants
- Required diameter of solid shaft
Recent comments
- 400000=120[14π(D2−10000)]
(…3 weeks 2 days ago - Use integration by parts for…1 month 3 weeks ago
- need answer1 month 3 weeks ago
- Yes you are absolutely right…1 month 3 weeks ago
- I think what is ask is the…1 month 3 weeks ago
- $\cos \theta = \dfrac{2}{…1 month 3 weeks ago
- Why did you use (1/SQ root 5…1 month 3 weeks ago
- How did you get the 300 000pi1 month 3 weeks ago
- It is not necessary to…1 month 3 weeks ago
- Draw a horizontal time line…1 month 4 weeks ago
$y(9x - 2y) \, dx - x(6x - y)
$y(9x - 2y) \, dx - x(6x - y) \, dy = 0$
y = vx
dy = v dx + x dv
$vx(9x - 2vx) \, dx - x(6x - vx)(v \, dx + x \, dv) = 0$
$vx(9x - 2vx) \, dx - vx(6x - vx)\, dx - x^2(6x - vx) \, dv = 0$
$vx(3x - 2vx) \, dx - x^2(6x - vx) \, dv = 0$
$vx^2(3 - 2v) \, dx - x^3(6 - v) \, dv = 0$
$\dfrac{x^2 \, dx}{x^3} - \dfrac{(6 - v) \, dv}{v(3 - 2v)} = 0$
$\dfrac{dx}{x} - \dfrac{(6 - v) \, dv}{v(3 - 2v)} = 0$
$\dfrac{6 - v}{v(3 - 2v)} = \dfrac{A}{v} + \dfrac{B}{3 - 2v}$
$6 - v = A(3 - 2v) + Bv$
When v = 0, A = 2
When v = 3/2, B = 3
$\dfrac{dx}{x} - \left( \dfrac{2}{v} + \dfrac{3}{3 - 2v} \right) \, dv = 0$
$\ln x - 2 \ln v + \frac{3}{2} \ln (3 - 2v) = ln c$
$\ln x - \ln v^2 + \ln (3 - 2v)^{3/2} = ln c$
$\ln \dfrac{x(3 - 2v)^{3/2}}{v^2} = ln c$
$\dfrac{x(3 - 2v)^{3/2}}{v^2} = c$
$\dfrac{x\left( 3 - \dfrac{2y}{x} \right)^{3/2}}{\dfrac{y^2}{x^2}} = c$
$\dfrac{x^3\left( \dfrac{3x - 2y}{x} \right)^{3/2}}{y^2} = c$
$\dfrac{x^3\left[ \dfrac{(3x - 2y)^{3/2}}{x^{3/2}} \right]}{y^2} = c$
$\dfrac{x^{3/2}(3x - 2y)^{3/2}}{y^2} = c$
$x^{3/2}(3x - 2y)^{3/2} = cy^2$ answer
parang ganito po yung factor
parang ganito po yung factor sa,
vx (9 x^2 - 2vx)dx - vx ( 6x - vx ) dx
9v x^2dx - 2 v^2 x^2dx - 6vx^2 dx + v^2x^2dx
(3x^2dv - v^2 x^2dx)
bakit po naging
bakit po naging
vx (3x -2vx) dx
Corrections:
Corrections:
$y(9x - 2y) \, dx - x(6x - y) \, dy = 0$
y = vx
dy = v dx + x dv
$vx(9x - 2vx) \, dx - x(6x - vx)(v \, dx + x \, dv) = 0$
$vx(9x - 2vx) \, dx - vx(6x - vx)\, dx - x^2(6x - vx) \, dv = 0$
$vx(3x - vx) \, dx - x^2(6x - vx) \, dv = 0$
$vx^2(3 - v) \, dx - x^3(6 - v) \, dv = 0$
$\dfrac{x^2 \, dx}{x^3} - \dfrac{(6 - v) \, dv}{v(3 - v)} = 0$
$\dfrac{dx}{x} - \dfrac{(6 - v) \, dv}{v(3 - v)} = 0$
$\dfrac{6 - v}{v(3 - v)} = \dfrac{A}{v} + \dfrac{B}{3 - v}$
$6 - v = A(3 - v) + Bv$
When v = 0, A = 2
When v = 3, B = 1
$\dfrac{dx}{x} - \left( \dfrac{2}{v} + \dfrac{1}{3 - v} \right) \, dv = 0$
$\ln x - 2 \ln v + \ln (3 - v) = ln c$
$\ln x - \ln v^2 + \ln (3 - v) = ln c$
$\ln \dfrac{x(3 - v)}{v^2} = ln c$
$\dfrac{x(3 - v)}{v^2} = c$
$\dfrac{x\left( 3 - \dfrac{y}{x} \right)}{\dfrac{y^2}{x^2}} = c$
$\dfrac{x^3\left( \dfrac{3x - y}{x} \right)}{y^2} = c$
$\dfrac{x^2(3x - y)}{y^2} = c$
$x^2(3x - y) = cy^2$ answer