Question

Solve the following Differential equations

a) x sin y dx + (x^2 + 1) cos y dy = 0

Answer #1

Solve the following differential equations.
a.) dy/dx+2xy=x, y(0)=2
b.) ?^2(dy/dx)−?y=−y^2

1. Solve the following differential equations.
(a) dy/dt +(1/t)y = cos(t) +(sin(t)/t) , y(2pie) = 1
(b)dy/dx = (2x + xy) / (y^2 + 1)
(c) dy/dx=(2xy^2 +1) / (2x^3y)
(d) dy/dx = y-x-1+(xiy+2) ^(-1)
2. A hollow sphere has a diameter of 8 ft. and is filled half way
with water. A circular hole (with a radius of 0.5 in.) is opened at
the bottom of the sphere. How long will it take for the sphere to
become empty?...

differential equations solve
(2xy+6x)dx+(x^2+4y^3)dy, y(0)=1

Solve the differential equation:
dy/dx = sin(x - y).

Solve the following differential equations
1. cos(t)y' - sin(t)y = t^2
2. y' - 2ty = t
Solve the ODE
3. ty' - y = t^3 e^(3t), for t > 0
Compare the number of solutions of the following three initial
value problems for the previous ODE
4. (i) y(1) = 1 (ii) y(0) = 1 (iii) y(0) = 0
Solve the IVP, and find the interval of validity of the
solution
5. y' + (cot x)y = 5e^(cos x),...

Solve the differential equation (5x^4 y^2+ 2xe^y - 2x cos (x^2)) dx
+ (2x^5y + x^2 e^y) dy = 0.

i)Please state if the following equations are exact or not:
(a) (sin(xy) − xy cos(xy))dx + x^2 cos(xy)dy = 0
(b) (x^3 + xy^2 )dx + (x^2 y + y^3 )dy = 0
ii) Determine if the following equation is exact, and if it is
exact, find its complete integral in the form g(x, y) = C:
(3(x)^2 + 2(y)^2 )dx + (4xy + 6(y)^2 )dy = 0

Solve the given differential equations:
a) dy/dx=(x+1)^2
b) (x+1)dy/dx-xy=x^2+x

Use the method for solving homogeneous equations to solve the
following differential equation.
(9x^2-y^2)dx+(xy-x^3y^-1)dy=0
solution is F(x,y)=C, Where C= ?

dx
+ (x cot y + sin y) dy=0, Solve the differential equation and write
your answer without negative exponents.

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