Question

Solve the following differential equations with initial conditions:

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

Answer #1

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

Given the second-order differential equation
y''(x) − xy'(x) + x^2 y(x) = 0
with initial conditions
y(0) = 0, y'(0) = 1.
(a) Write this equation as a system of 2 first order
differential equations.
(b) Approximate its solution by using the forward Euler
method.

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

Solve the following initial-value differential
equations using Laplace and inverse transformation.
y''' +y' =0, y(0)=1, y'(0)=2, y''(0)=1

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

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
y^' − xy = e^x y(0) = 2

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

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