Question

Solve the following differential equations through order reduction.

(a) xy′y′′−3ln(x)((y′)2−1)=0.

(b) y′′−2ln(1−x)y′=x.

Answer #1

a

Solve the 2nd Order Differential Equation using METHOD OF
REDUCTION
Please don't skip steps!
(x-1)y"-xy'+y=0 x>1 y1(x)=x

Solve the following non-linear differential equations.
y'=xy''-x(y')^2

Solve the 2nd Order
Differential Equation using METHOD OF REDUCTION
Please don't skip
steps!
(x-1)y"-xy'+y=0 x>1
y1(x)=x
My professor is
getting y2(x)=e^x and I don't understand how!

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 following differential equations
y''-4y'+4y=(x+1)e2x (Use Wronskian)
y''+(y')2+1=0 (non linear second order equation)

Solve the following differential equations with initial
conditions:
xy'-y=3xy1/2

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

(61). (Bernoulli’s Equation): Find the general solution of the
following first-order differential equations:(a) x(dy/dx)+y=
y^2+ln(x) (b) (1/y^2)(dy/dx)+(1/xy)=1

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