Numerical Value Questions

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1.
Solve dy/dx + y = 1 with y(0) = 0. Find y(ln 2).
2.
Solve dy/dx = (x + y)/x with y(1) = 1. Find y(e).
3.
For the Bernoulli equation dy/dx - y = -y^3, with v = y^(-2), the resulting linear equation is dv/dx + av = b. Find a.
4.
Solve (2xy + 3) dx + (x^2 + 4y) dy = 0. If the solution passes through (1, 0), find the value of the constant.
5.
For the DE dy/dx + (3x^2/(1+x^3))*y = sin^2(x)/(1+x^3), the integrating factor at x = 0 is:

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