Question

x’+2x=sin(t), x(0)=1

solve the first order differential equation.

Answer #1

Solve the first-order linear differential equation:
y ′ + sin ( x ) y = sin ( x ) , y ( 0 ) = 2.

Solve the first order differential equation.
y' - y= sin(x)

Solve the first order homogeneous differential equation:
(2x-5y)dx + (4x-y) dy=0

Use undetermined coefficients to solve the differential
equation
y'' + y = x sin 2x

Solve the differential equation y"-4y'-12y=sin(2x)

Solve the differential equation by variation of parameters.
y'' + 4y = sin(2x)

Consider the differential equation x′=[2 −2 4 −2], with x(0)=[1
1] Solve the differential equation wherex=[x(t)y(t)]
please write as neat as possible better if typed and explain
clearly with step by step work

(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 initial/boundary value problem:
∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π,
u(t,0)=u(t,π)=0 for t>0,
u(0,x)=sin^2x for 0≤x≤ π.
if you like, you can use/cite the solution of Fourier sine
series of sin^2(x) on [0,pi] = 1/4-(1/4)cos(2x)
please show all steps and work clearly so I can follow your
logic and learn to solve similar ones myself.

dx
+ (x cot y + sin y) dy=0, Solve the differential equation and write
your answer without negative exponents.

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