Question

Solve the following differential equations

y''-4y'+4y=(x+1)e^{2x} (Use Wronskian)

y''+(y')^{2}+1=0 (non linear second order equation)

Answer #1

Write the second order differential equation as a system of two
linear differential equations then solve it.
x''-6x'+13x=0 x(0)= -1 x'(0)=1

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

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

Solve the initial-value problem for linear differential
equation
y'' + 4y' + 8y = sinx; y(0) = 1,
y'(0) = 0

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

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.

(differential equations): solve for x(t) and y(t)
2x' + x - (5y' +4y)=0
3x'-2x-(4y'-y)=0
note: Prime denotes d/dt

Solve the following differential equations using inspection:
1) y”+4y=12
2) y””+4y”+4y=-20
3) (D^4 -4D^2)y=24
4) y”-y=x-1
5) D(D-3)y=4
6) (D^2+2D-8)(D+3)y=0
7) y”-y’-2y=18xe^(2x)

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 the second-order linear differential equation
y′′ − 2y′ − 3y = −32e−x using the method of variation of
parameters.

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