1. Find a particular solution of a linear homogeneous differential equation.
1.12 y + 3y + 3y + y = 0, y (0) = -1, y (0) = 0, y (0) = 1
2. Solve the system of differential equations in two ways: a) information to higher order differential equations; b) using a characteristic equation.
2.12 x ´= 4x + 2y, y´ = 4x + 6y
3. Solve the differential equation by variation of arbitrary constants.
3.12 y + y = tgx
4. Solve the following problems.
4.12 Write the equation of the curve passing through the point A (1, 2) and has the following property: the ratio of the ordinates of any point in the abscissa of this point is proportional to the slope of the tangent to the desired curve drawn at the same point. The proportionality coefficient is equal to 3.
Detailed solution. Decorated in Microsoft Word 2003. (Target decided to use formula editor)
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