Réitigh x+yy^prime=f(x)g(sqrt{x^2+y^2})

$$x + y y ^ { \prime } = f ( x ) g ( \sqrt { x ^ { 2 } + y ^ { 2 } } )$$

Réitigh do f. (complex solution)

$$\left\{\begin{matrix}f=\frac{\left(x^{2}+y^{2}\right)^{-\frac{1}{2}}}{g}\text{, }&x\neq iy\text{ and }x\neq -iy\text{ and }g\neq 0\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$fxg\sqrt{x^{2}+y^{2}}=x+y\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$gx\sqrt{x^{2}+y^{2}}f=x$$

Roinn an dá thaobh faoi xg\sqrt{x^{2}+y^{2}}.

$$\frac{gx\sqrt{x^{2}+y^{2}}f}{gx\sqrt{x^{2}+y^{2}}}=\frac{x}{gx\sqrt{x^{2}+y^{2}}}$$

Má roinntear é faoi xg\sqrt{x^{2}+y^{2}} cuirtear an iolrúchán faoi xg\sqrt{x^{2}+y^{2}} ar ceal.

$$f=\frac{x}{gx\sqrt{x^{2}+y^{2}}}$$

Roinn x faoi xg\sqrt{x^{2}+y^{2}}.

$$f=\frac{\left(x^{2}+y^{2}\right)^{-\frac{1}{2}}}{g}$$

Réitigh do g. (complex solution)

$$\left\{\begin{matrix}g=\frac{\left(x^{2}+y^{2}\right)^{-\frac{1}{2}}}{f}\text{, }&x\neq iy\text{ and }x\neq -iy\text{ and }f\neq 0\\g\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$fxg\sqrt{x^{2}+y^{2}}=x+y\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$fx\sqrt{x^{2}+y^{2}}g=x$$

Roinn an dá thaobh faoi fx\sqrt{x^{2}+y^{2}}.

$$\frac{fx\sqrt{x^{2}+y^{2}}g}{fx\sqrt{x^{2}+y^{2}}}=\frac{x}{fx\sqrt{x^{2}+y^{2}}}$$

Má roinntear é faoi fx\sqrt{x^{2}+y^{2}} cuirtear an iolrúchán faoi fx\sqrt{x^{2}+y^{2}} ar ceal.

$$g=\frac{x}{fx\sqrt{x^{2}+y^{2}}}$$

Roinn x faoi fx\sqrt{x^{2}+y^{2}}.

$$g=\frac{\left(x^{2}+y^{2}\right)^{-\frac{1}{2}}}{f}$$

Réitigh do f.

$$\left\{\begin{matrix}f=\frac{1}{g\sqrt{x^{2}+y^{2}}}\text{, }&g\neq 0\text{ and }x\neq 0\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$fxg\sqrt{x^{2}+y^{2}}=x+y\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$gx\sqrt{x^{2}+y^{2}}f=x$$

Roinn an dá thaobh faoi xg\sqrt{x^{2}+y^{2}}.

$$\frac{gx\sqrt{x^{2}+y^{2}}f}{gx\sqrt{x^{2}+y^{2}}}=\frac{x}{gx\sqrt{x^{2}+y^{2}}}$$

Má roinntear é faoi xg\sqrt{x^{2}+y^{2}} cuirtear an iolrúchán faoi xg\sqrt{x^{2}+y^{2}} ar ceal.

$$f=\frac{x}{gx\sqrt{x^{2}+y^{2}}}$$

Roinn x faoi xg\sqrt{x^{2}+y^{2}}.

$$f=\frac{1}{g\sqrt{x^{2}+y^{2}}}$$

Réitigh do g.

$$\left\{\begin{matrix}g=\frac{1}{f\sqrt{x^{2}+y^{2}}}\text{, }&x\neq 0\text{ and }f\neq 0\\g\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$fxg\sqrt{x^{2}+y^{2}}=x+y\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$fx\sqrt{x^{2}+y^{2}}g=x$$

Roinn an dá thaobh faoi fx\sqrt{x^{2}+y^{2}}.

$$\frac{fx\sqrt{x^{2}+y^{2}}g}{fx\sqrt{x^{2}+y^{2}}}=\frac{x}{fx\sqrt{x^{2}+y^{2}}}$$

Má roinntear é faoi fx\sqrt{x^{2}+y^{2}} cuirtear an iolrúchán faoi fx\sqrt{x^{2}+y^{2}} ar ceal.

$$g=\frac{x}{fx\sqrt{x^{2}+y^{2}}}$$

Roinn x faoi fx\sqrt{x^{2}+y^{2}}.

$$g=\frac{1}{f\sqrt{x^{2}+y^{2}}}$$