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5. Find the general solution to the differential equation y'' + y= sin2 x
f(t) = h(t − 1) + h(t − 3)
for t ≥ 0, where h(t) is the Heaviside step function.
Solve the differential equation of the following linear differential equations. Show step-by-step procedures.
dy/dx + y = e2x
Solve the differential equation of the following exact differential equation. Show complete solution.
(3x2y - 6x)dx + (x3 + 2y)dy = 0
Find the differential equations of the following equations by integrating factors by inspection. Show complete solution.
ydx + (x + x^3 y^2)dy = 0
Find the differential equations of the following equations by integrating factors by inspection. Show complete solution.
xdy - ydx = x^4 ydy + x^3 y^2dx
Solve the differential equation of the following homogeneous equation. Show complete solution.
x dy/dx + y = x^3
Solve the differential equation of the following homogeneous equation. Show complete solution.
(3x^2 y - 6x)dx + (x^3 + 2y)dy = 0
Solve the differential equation of the following linear differential equations. Show complete solution.
dy/dx + y = e^2x
