Question

Solve the following non-linear differential equations.

y'=xy''-x(y')^2

Answer #1

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 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 differential equation
(x^2)y'' - xy' +y =2x

Introduction to differential equations
1. y' = x-1+xy-y
2. x^2 y' - yx^2 = y

Homogeneous Differential Equations:
dy/dx = xy/x^(2) - y^(2)
dy/dx = x^2 + y^2 / 2xy

Simplify the following non linear equations to linear form.
label the slope and y intercept
y=ax^4+b
y=ax^b+5
xy=10^a(x^2+y^2)+b
sinx=(a+by/siny)

Solve the following Bernoulli equations:
1) (2+x^2)y' +xy=x^3y^3
2) y′(x) + y/(x-2) = 5(x − 2)y^(1/2)

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