`1,1`
`2,1`
`4,1`
`1,4`
`(d^2y)/(dx^2) - 8 (dy)/(dx) + 15 y = 0`
`(d^2y)/(dx^2) + 8 (dy)/(dx) + 15 y = 0`
`(d^2y)/(dx^2) + 8 (dy)/(dx) - 15 y = 0`
None of these
` P(x)`
`P(x)p'(x)`
`P (x) P'''(x)`
constant
`tan y tan x = c`
`(tany)/(tanx) = C`
`(tan^2 x) /(tany) = C`
None of these
`tan (x^2 + y^2) = x^2/y^2 + C`
`cot (x^2 + y^2) = x^2/y^2 + C`
`tan (x^2 + y^2) = y^2/x^2 + C`
`cot (x^2 + y^2) = x^2/y^2 + C`
`0`
`3`
`1`
`2`
`tan^(-1) x`
`1+x^2`
`e^(tan^(-1) x)`
`log_e(1+x^2)`
`m = 3, n = 3`
`m = 3, n = 2`
`m = 3, n = 5`
`m = 3, n = 1`
order 1, degree 3
order 2, degree 2
degree 3, order 3
degree 4, order 4
`y={phi(x) - 1} + Ce^(-phi(x))`
`y phi(x) = {phi(x)}^2+C`
`ye^(phi(x)) = phi(x) e^(phi(x)) +C`
`y-phi(x)e^(-phi(x))`
`y^3 = x^3 log cx`
`y^3 = 3x^3 log cx`
`x^3 = 3x^3 log cx`
`y^3 = 3x^3 log x`
`y = log_e (x) + C`
`y = (log_e x)^2 + C`
` y = pm sqrt ( (log_e x)^2 + 2C )`
`xy = x^y + K`
`2`
`3`
`1`
None of these
`log tan(y/2)=C-2 sin x`
`log tan (y/4)=C-2 sin(x/2)`
`log tan (y/2+pi/4)=C-2 sin x`
`log tan (y/2+pi/4)=C-2 sin (x/2)`
`(a + m) y = e^(mx) + ce^(−ax)`
`y = e^(mx) + ce^(−ax)`
`(a + m) y = e^(mx) + c`
`ye^(ax) = me^(mx) + c`
`x^2 + y^2 = xC`
`x^2 - y^2 = xC`
`x^2 + y^2 = C`
`x^2 - y^2 = C`
`y - sqrt (x^2 + y^2) = Cx^2`
`y + sqrt (x^2 + y^2) = Cx^2`
`y + sqrt(x^2 + y^2) +Cx^2 = 0`
none of the above
`(d^2y)/(dx^2) + 8 (dy)/(dx) + 15 y = 0`
`(d^2y)/(dx^2) - 8 (dy)/(dx) + 15 y = 0`
`(d^2y)/(dx^2) - (dy)/(dx) + y = 0`
None of these
`(log_e x)^3`
`log_e (log_e x)`
`log_e x`
`(log_e x)^(1//3)`
` xy (dy)/(dx) - x^2 + y^2 = 0`
` 2xy (dy)/(dx) - x^2 - y^2 = 0`
`(x^2 + y^2) (dy)/(dx) - 2xy = 0`
None of the above
`(x^2 - y^2 ) (dy)/(dx) + 2xy = 0`
`(x^2 - y^2) (dy)/(dx) = 2xy`
`(x^2 - y^2) (dy)/(dx) = xy`
`(x^2 - y^2) (dy)/(dx) + xy = 0`