Mathematics · Partial Differential Equations
Which of the following options represents the general solution of the partial differential equation uxx - 2 sin x · uxy - cos2x · uyy - cos x · uy = 0?
- 1u(x, y) = φ(x - y - cos x) + ψ(xy + cos x)
- 2u(x, y) = φ(x + y - cos x) + ψ(x + y cos x)
- 3u(x, y) = φ(x + y - cos x) + ψ(x - y + cos x)✓
- 4u(x, y) = φ(x + y + cos x) + ψ(x - y - cos x)
Correct answer
u(x, y) = φ(x + y - cos x) + ψ(x - y + cos x)
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