IDZ 11.2 - Option 8. Decisions Ryabushko AP
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8v-IDZ11.2.pdf (99.62 KB)
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09.07.2025
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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 to the nearest two decimal places.
- 1.8 y´´´ = e2x, x0 = 1/2, y (0) = 9/8, y´(0) = 1/4, y´´ (0) = -1/2.
- 2. Find the general solution of the differential equation that admit a lowering of the order
- 2.8 x2y´´ + xy´ = 1
- 3. Solve the Cauchy problem for differential equations admitting a reduction of order.
- 3.8 y´´ = -1 / (2y3), y (0) = 1/2, y´(0) = √2.
- 4. Integrate the following equation.
- 4.8 (1 - ex / y) dx + ex / y (1 - x / y) dy = 0
- 5. Write the equation of the curve passing through the point A (x0, y0), if it is known that the slope of the tangent at any point in n is greater than the slope of the straight line connecting the same point with the origin.
- 5.8 A (3, -1), n = 3/2
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