Solve dx/dx=(3x4)/y+312/2

$$\frac { d x } { d x } = \frac { ( 3 x 4 ) } { y } + \frac { 312 } { 2 }$$

Solve for x_4

$$x_{4}=-\frac{155y}{3}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y, the least common multiple of y,2.

$$2y\frac{\mathrm{d}}{\mathrm{d}x}(x)=2\times 3x_{4}+y\times 312$$

Multiply 2 and 3 to get 6.

$$2y\frac{\mathrm{d}}{\mathrm{d}x}(x)=6x_{4}+y\times 312$$

Swap sides so that all variable terms are on the left hand side.

$$6x_{4}+y\times 312=2y\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

Subtract y\times 312 from both sides.

$$6x_{4}=2y\frac{\mathrm{d}}{\mathrm{d}x}(x)-y\times 312$$

Multiply -1 and 312 to get -312.

$$6x_{4}=2y\frac{\mathrm{d}}{\mathrm{d}x}(x)-312y$$

The equation is in standard form.

$$6x_{4}=-310y$$

Divide both sides by 6.

$$\frac{6x_{4}}{6}=-\frac{310y}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x_{4}=-\frac{310y}{6}$$

Divide -310y by 6.

$$x_{4}=-\frac{155y}{3}$$

Solve for x

$$x\in \mathrm{R}$$

$$x_{4}=-\frac{155y}{3}\text{ and }y\neq 0$$