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If `y_1` and `y_2` are the solution of the differential equation `(dy)/(dx)+P y=Q` , where `P` and `Q` are functions of `x` alone and `y_2=y_1z` , then prove that `z=1+c.e` where `c` is an arbitrary constant.

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CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
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  12. The solution of the equation (dy)/(dx)=(x(2logx+1))/(siny+ycosy) is

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  13. The solution of the equation log ((dy)/(dx))=a x+b y is

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  14. If y=y(x) and (2+sinx)/(y+1)((dy)/(dx))=-cosx ,y(0)=1, then y(pi/2) ...

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  15. The equation of the curves through the point (1, 0) and whose slope...

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  16. The solution of (d v)/(dt)+k/m v=-g is

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  17. The solution of the equation (dy)/(dx)=cos(x-y) is

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  18. The solution of the equation (x^2y+x^2)dx+y^2(x-1)dy=0 is given by

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  19. Solution of differential equation dy-sinxsiny dx=0 is

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  20. Solution of (dy)/(dx)+2x y=y is

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