Solve ∫ 3/x-4/y=-7

$$\int \frac { 3 } { x } - \frac { 4 } { y } = - 7$$

Solve for y

$$y=\frac{4}{3\ln(|x|)+С}$$

$$x\neq 0\text{ and }|x|\neq e^{-\frac{С}{3}}$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$y\int \frac{3}{x}\mathrm{d}x-4=-7y$$

Add 7y to both sides.

$$y\int \frac{3}{x}\mathrm{d}x-4+7y=0$$

Add 4 to both sides. Anything plus zero gives itself.

$$y\int \frac{3}{x}\mathrm{d}x+7y=4$$

Combine all terms containing y.

$$\left(\int \frac{3}{x}\mathrm{d}x+7\right)y=4$$

The equation is in standard form.

$$\left(3\ln(|x|)+С\right)y=4$$

Divide both sides by 3\ln(|x|)+С.

$$\frac{\left(3\ln(|x|)+С\right)y}{3\ln(|x|)+С}=\frac{4}{3\ln(|x|)+С}$$

Dividing by 3\ln(|x|)+С undoes the multiplication by 3\ln(|x|)+С.

$$y=\frac{4}{3\ln(|x|)+С}$$

Variable y cannot be equal to 0.

$$y=\frac{4}{3\ln(|x|)+С}\text{, }y\neq 0$$