Learn more about our help with Assignments: Differential Equations
Search & Filtering
Differential Equations
Solve the following with the help of Banoulli equation?
dy/dx + y/2x = x/y^3
dy/dx + y/2x = x/y^3
Differential Equations
Differentiate the following functions
y = (〖6x〗^3+〖4x〗^2+3)(〖2x〗^2-〖4x〗^(-2)+5)
y = (〖6x〗^3+〖4x〗^2+3)(〖2x〗^2-〖4x〗^(-2)+5)
Differential Equations
Given the following monotonically transformed utility function faced by the consumer
lnU(X1X2) = ∝lnX1+βlnX2
The price of good X1 is P1 and the price of good X2 is P2.
Construct the corresponding Langregian function
Derive the optimal demand (Marshallian demand) function for X1 and for X2.
lnU(X1X2) = ∝lnX1+βlnX2
The price of good X1 is P1 and the price of good X2 is P2.
Construct the corresponding Langregian function
Derive the optimal demand (Marshallian demand) function for X1 and for X2.
Differential Equations
(a) Differentiate the following function
y = x^2 e^x
(b) A cosmetic company is planning the introduction of a promotion of a new lipstick line. The marketing research department after test marketing the new line in a carefully selected city found that the demand in the city is approximately given by p = 12e^(-x), where x which should be within this range, 0 ≤ x ≤ 2 were thousand lipsticks sold per week at a price of Kenya shillings. At what price will the weekly revenue be at maximum? What is the maximum weekly revenue
y = x^2 e^x
(b) A cosmetic company is planning the introduction of a promotion of a new lipstick line. The marketing research department after test marketing the new line in a carefully selected city found that the demand in the city is approximately given by p = 12e^(-x), where x which should be within this range, 0 ≤ x ≤ 2 were thousand lipsticks sold per week at a price of Kenya shillings. At what price will the weekly revenue be at maximum? What is the maximum weekly revenue
Differential Equations
Separate the following partial differential equation into a set of three ODEs by the method of separation of variables :
d^2 u/dt^2 = c^2 [d^2 u/dr^2 + 1/r * du/dr + 1/r^2 * d^2/d(thita)^2 ]
d^2 u/dt^2 = c^2 [d^2 u/dr^2 + 1/r * du/dr + 1/r^2 * d^2/d(thita)^2 ]
Differential Equations
Separate the following partial differential equation into a set of three ODEs by the method of separation of variables :
d(do)^2 u /d(do)t^2 =C^2[d(do)^2 u /d(do) r^2 +1 du /r dr +1 /r^2 d^2 u /d (thita) ^2]
d(do)^2 u /d(do)t^2 =C^2[d(do)^2 u /d(do) r^2 +1 du /r dr +1 /r^2 d^2 u /d (thita) ^2]
Differential Equations
Solve: z(p-q)=z^2 + (x+y^2)
Differential Equations
9. a) Find f ( y) so that equation f (y)dx − zx dy − xy ln y dz = 0 is integrable. Also obtain
the corresponding integral using Natani’s method.
b) Find the differential equation of the family of surfaces
phi [z (x + y)^2 , x^2 - y^2]=0
the corresponding integral using Natani’s method.
b) Find the differential equation of the family of surfaces
phi [z (x + y)^2 , x^2 - y^2]=0
Differential Equations
8. a) Solve the differential equation x^3 p^2 + x^2 yp + a^3 = 0 and also obtain its singular solution, if
it exists.
b) The differential equation satisfied by a beam uniformly loaded (W kg /meter) , with one
end fixed and the second end subjected to a tensile force-P, is given by
EI (d^2 y / d x^2) = Py - 1/2 W x^2 ,
where E is the modulus of elasticity and I is the moment of inertia. Show that the elastic
curve for the beam with conditions y = 0 and dy/dx = 0 at x = 0 , is given by
y = W / Pn^2 (1-cosh nx) + W x^2 / 2P , where n^2 = (P/EI)
c) For 0 < x < 5 and t > 0 , solve the one-dimensional heat flow equation d u/d t = 4 d^2 u/ d x^2
satisfying the conditions u(t, 0) = u(t,5) = 0, u(0, x) = x
it exists.
b) The differential equation satisfied by a beam uniformly loaded (W kg /meter) , with one
end fixed and the second end subjected to a tensile force-P, is given by
EI (d^2 y / d x^2) = Py - 1/2 W x^2 ,
where E is the modulus of elasticity and I is the moment of inertia. Show that the elastic
curve for the beam with conditions y = 0 and dy/dx = 0 at x = 0 , is given by
y = W / Pn^2 (1-cosh nx) + W x^2 / 2P , where n^2 = (P/EI)
c) For 0 < x < 5 and t > 0 , solve the one-dimensional heat flow equation d u/d t = 4 d^2 u/ d x^2
satisfying the conditions u(t, 0) = u(t,5) = 0, u(0, x) = x
Differential Equations
9. a) Find f ( y) so that equation f (y)dx − zx dy − xy ln y dz = 0 is integrable. Also obtain
the corresponding integral using Natani’s method.
b) Find the differential equation of the family of surfaces: theta [ z (x+y)^2 , x^2 - y^2 ] = 0.
the corresponding integral using Natani’s method.
b) Find the differential equation of the family of surfaces: theta [ z (x+y)^2 , x^2 - y^2 ] = 0.
