What is the solution for 2xdz-2zdx=sqrt(x^2+4z^2)dx ?

The solution for 2xdz-2zdx=sqrt(x^2+4z^2)dx is z=-1/(4e^{2c_{1)}}+(e^{2c_{1}}x^2)/4

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2xdz-2zdx=sqrt(x^2+4z^2)dx

2 x d z - 2 z d x = x^{2} + 4 z^{2} d x

z = - \frac{1}{4 e ^{2 c_{1}}} + \frac{e ^{2 c_{1}} x ^{2}}{4}

Solution steps

2 x d z - 2 z d x = x^{2} + 4 z^{2} d x

Solve using substitution:

z = - \frac{1}{4 e ^{2 c_{1}}} + \frac{e ^{2 c_{1}} x ^{2}}{4}

z = - \frac{1}{4 e ^{2 c_{1}}} + \frac{e ^{2 c_{1}} x ^{2}}{4}

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What is the solution for 2xdz-2zdx=sqrt(x^2+4z^2)dx ?
The solution for 2xdz-2zdx=sqrt(x^2+4z^2)dx is z=-1/(4e^{2c_{1)}}+(e^{2c_{1}}x^2)/4