Solve xy^prime-(1-x)y+my=0

$$x y ^ { \prime } - ( 1 - x ) y + m y = 0$$

Solve for m

$$\left\{\begin{matrix}m=1-x\text{, }&y\neq 0\\m\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-x by y.

$$x\frac{\mathrm{d}}{\mathrm{d}x}(y)-\left(y-xy\right)+my=0$$

To find the opposite of y-xy, find the opposite of each term.

$$x\frac{\mathrm{d}}{\mathrm{d}x}(y)-y+xy+my=0$$

Subtract x\frac{\mathrm{d}}{\mathrm{d}x}(y) from both sides. Anything subtracted from zero gives its negation.

$$-y+xy+my=-x\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Add y to both sides.

$$xy+my=-x\frac{\mathrm{d}}{\mathrm{d}x}(y)+y$$

Subtract xy from both sides.

$$my=-x\frac{\mathrm{d}}{\mathrm{d}x}(y)+y-xy$$

Reorder the terms.

$$my=-x\frac{\mathrm{d}}{\mathrm{d}x}(y)-xy+y$$

The equation is in standard form.

$$ym=y-xy$$

Divide both sides by y.

$$\frac{ym}{y}=\frac{y-xy}{y}$$

Dividing by y undoes the multiplication by y.

$$m=\frac{y-xy}{y}$$

Divide -yx+y by y.

$$m=1-x$$

Solve for x

$$\left\{\begin{matrix}x=1-m\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$