Reshebnik Ryabushko. Solved IDZ 11.2, Option 13
Replenishment date: 01.09.2020
Content: 13v-IDZ11.2.rar (62.07 KB)
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1. Find a particular solution of the differential equation and calculate the value of the resulting function y = φ (x) at x = x0 accurate to two decimal places.
1.13 y´´ = arctgx, x0 = 1, y (0) = y´ (0) = 0.
2. Find the general solution of a differential equation admitting a lowering of the order
2.13 xy´´ = y´ln (y´ / x)
3. Solve the Cauchy problem for a differential equation admitting a reduction in order.
3.13 y´´ = 1 / y3, y (0) = 1, y´ (0) = 0.
4. Integrate the following equations.
4.13 (2x+(x2+y2)/(x2+y))dx=((x2+y2)/(xy2))dy
5. Write down the equation of the curve passing through the point A (x0, y0) if it is known that the length of the segment cut off on the ordinate by the normal drawn at any point of the curve is equal to the distance from this point to the origin.
5.13 A (0, 1)
1.13 y´´ = arctgx, x0 = 1, y (0) = y´ (0) = 0.
2. Find the general solution of a differential equation admitting a lowering of the order
2.13 xy´´ = y´ln (y´ / x)
3. Solve the Cauchy problem for a differential equation admitting a reduction in order.
3.13 y´´ = 1 / y3, y (0) = 1, y´ (0) = 0.
4. Integrate the following equations.
4.13 (2x+(x2+y2)/(x2+y))dx=((x2+y2)/(xy2))dy
5. Write down the equation of the curve passing through the point A (x0, y0) if it is known that the length of the segment cut off on the ordinate by the normal drawn at any point of the curve is equal to the distance from this point to the origin.
5.13 A (0, 1)
Additional Information
The solution is executed in Microsoft Word 2003. The document with the IDZ solution is archived in the WinRar program.