Answer to Question #79369 in Differential Equations for Prince

Question #79369

Which of the following satisfied the Laplace's equation in the plane
1. x^2 + y^2
2. x^2 - y^2
3. x + y
4. x - y

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1. (x^2+y^2)dx − 2xydy=0 −x^2−y^2=cx −x^2+y^2=cx x^2+y^2=cx x^2−y^2=cx
2. Integration factor 1. (x + 2y) dx + x dy = 0 2. ((x^2) + (y^2) + x) dx + y dy = 0 3. (5y - 6x)
3. Exact equations (e^(x^2)y)(1+2(x^2)y)dx + (x^3)(e^(x^2)y)dy = 0 Integrating factor 1. (2xy) dx
4. 2. Solve the initial value problem (1+y^2)dx+(1+x^2)d,y(0)=−1 Tan^−1 x−tan^−1 y=−π/4 T
5. if Uxx + Uyy=0 in x^2 + y^2=1 and U = 3+x+y find U(1/2, 1/2) A)0 B)2 C)3 D)4
6. 1. Find the solution of y′=2xy^2 y=1/2x(1−y^2) y=1/2x(1+y^2) y=1/2(1−y^2) y=1/2x^2(1�
7. Solve the general solution of dy/dx =ex + x + sinx

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