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For each of the following differential e...

For each of the following differential equations verify that the accompanying functions a solution. Differential Function `x(dy)/(dx)=y` `y=a x` `x+y(dy)/(dx)=0` `y=+-sqrt(a^2-x^2)` `x(dy)/(dx)y=y^2` `y=a/(x+a)` `x^3(d^2y)/(dx^2)=1` `y=a x+b+1/(2x)` `y=((dy)/(dx))^2` `y=1/4(x+-a)^2`

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For each of the following differential equations verify that the accompanying functions a solution. (i) x(dy)/(dx)=y => y=a x (ii) x+y(dy)/(dx)=0 => y=+-sqrt(a^2-x^2) (iii) x(dy)/(dx)y+y^2 => y=a/(x+a) (iv) x^3(d^2y)/(dx^2)=1 => y=a x+b+1/(2x) (v) y=((dy)/(dx))^2 => y=1/4(x+-a)^2

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