REVIEW PROBLEMS In Problems 1-30, solve the equation. 1. dy/dx = e^(x+y) / (y - 1) 2. dy/dx - 4y = 32 3. (x^2 - 2y^-3)dy + (2xy - 3x^2)dx = 0 4. dy/dx + 3y/x = x^2 - 4x + 3 5. [sin(xy) + xy cos(xy)]dx + [1 + x^2cos(xy)]dy 6. 2xy^3 dx - (1 - x^2)dy = 0 7. t^3y^2 dt + t^4y^-6 dy = 0 8. dy/dx + 2y/x = 2x^2y^2 9. (x^2 + y^2)dx + 3xy dy = 0 10. [1 + (1 + x^2 + 2xy + y^2)^-1] dx + [y^-1/2 + (1 + x^2 + 2xy + y^2)^-1] dy 11. dx/dt = 1 + cos^2(t - x) 12. (y^3 + 4e^x y)dx + (2e^x + 3y^2)dy = 0
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Step 1: Find the integrating factor for the differential equation \( \frac{d^2y}{dx^2} - 4y = \frac{33}{9} \). Show more…
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