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[单选题]
微分方程dy/dx=xy的通解为()
A.y=ce^2x
B.y=Ce^1/2x^2
C.y=e^Cx
D.y=Ce^x^2
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A.y=ce^2x
B.y=Ce^1/2x^2
C.y=e^Cx
D.y=Ce^x^2
A.y=dsolve(y '=x+y+1')
B.y=dsolve('Dy=x+y+1')
C.y=dsolve('Dy=x+y+1'; 'x')
D.y=dsolve('Y'=x+y+1', 'x')
验证下列微分方程为全微分方程,并求其解:
(1)(1-4xy)dy=(2y2-3x2)dx;
(2)(3x2y2-4xy)dy+(2xy3-2y2)dx=0;
(3)(x+y2)y'=2x2-y;
(4)xy2dx=(y3-x2y)dy。
求出常系数非齐次线性方程组dy/dx=Ay+f(x)的通解,其中:
(1)
(2)
(3)