Question

Solve the following differential equations with initial conditions:

xy'-y=3xy^{1/2}

Answer #1

Solve the following differential equations through order
reduction.
(a) xy′y′′−3ln(x)((y′)2−1)=0.
(b) y′′−2ln(1−x)y′=x.

solve differential equation ((x)2 - xy +(y)2)dx - xydy
= 0
solve differential equation (x^2-xy+y^2)dx - xydy =
0

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= ?

Solve the system of differential equations using Laplace
transform:
y'' + x + y = 0
x' + y' = 0
with initial conditions
y'(0) = 0
y(0) = 0
x(0) = 1

solve the differential equation
xy'+y=4x3y2lnx

Solve the differential equation.
xy + y' = 76x

Solve each of the following equations. Implicit answers are
acceptable.
a.) y'-y= cos(x)
with no initial conditions and:
b.) y'= e(x)y-1
with initial conditions y(0)=0

Solve the Homogeneous differential equation
(7 y^2 + 1 xy)dx - 1 x^2 dy = 0
(a) A one-parameter family of solution of the equation is y(x)
=
(b) The particular solution of the equation subject to the
initial condition y(1) =1/7.

Solve the following differential equation using taylor series
centered at x=0:
(2+x^2)y''-xy'+4y = 0

Solve the differential equations
(2D^2 + D - 3)y = 2x - 3x^2

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