Solve y^prime=-a*1/x^2+3*2x/x^4=

$$y ^ { \prime } = \frac { - a \cdot 1 } { x ^ { 2 } } + \frac { 3 \cdot 2 x } { x ^ { 4 } } =$$

Solve for a

$$a=\frac{6}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{4}, the least common multiple of x^{2},x^{4}.

$$x^{4}\frac{\mathrm{d}}{\mathrm{d}x}(y)=x^{2}\left(-a\right)\times 1+3\times 2x$$

Multiply 3 and 2 to get 6.

$$x^{4}\frac{\mathrm{d}}{\mathrm{d}x}(y)=x^{2}\left(-a\right)\times 1+6x$$

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

$$x^{2}\left(-a\right)\times 1+6x=x^{4}\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Subtract 6x from both sides.

$$x^{2}\left(-a\right)\times 1=x^{4}\frac{\mathrm{d}}{\mathrm{d}x}(y)-6x$$

Reorder the terms.

$$\left(-a\right)x^{2}=x^{4}\frac{\mathrm{d}}{\mathrm{d}x}(y)-6x$$

Reorder the terms.

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

The equation is in standard form.

$$\left(-x^{2}\right)a=-6x$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)a}{-x^{2}}=-\frac{6x}{-x^{2}}$$

Dividing by -x^{2} undoes the multiplication by -x^{2}.

$$a=-\frac{6x}{-x^{2}}$$

Divide -6x by -x^{2}.

$$a=\frac{6}{x}$$

Solve for x

$$x=\frac{6}{a}$$

$$a\neq 0$$