InterviewSolution
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InterviewSolution
| 1. |
Solve the differential equation `(1 + x^(2))dy+2xydx = sin^(2) x dx` |
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Answer» `(dy)/(dx) + (2x)/(1+x^(2))y = (sin^(2)x)/(1 + x^(2))` ...(1) Equation (1) is the linear differential equation of the type `(dy)/(dx) + Py = Q`, where `P = (2x)/(1+x^(2))` and `Q = (sin^(2)x)/(1+x^(2))` `:. I.F. = e^(int(2x)/(1+x^(2))dx)` `= e^(ln(1+x^(2)))` `= 1 + x^(2)` Thus, the solution of (1) is `y(1+x^(2)) = int (sin^(2)x)/(1+x^(2))(1+x^(2))dx + c` `= (1)/(2)int(1-cos 2x)dx + c` `rArr y(1+x^(2)) = (1)/(2)(x-(sin 2x)/(2))+c` |
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