Solve frac{4R_{1}}{R_{2}}d^2r/dt^2+frac{12*R_{1}}{R_{2}}dr/dt=q

$$\frac { 4 R _ { 1 } } { R _ { 2 } } \frac { d ^ { 2 } r } { d t ^ { 2 } } + \frac { 12 \cdot R _ { 1 } } { R _ { 2 } } \frac { d r } { d t } = q$$

Solve for R_1 (complex solution)

$$R_{1}\in \mathrm{C}$$

$$q=0\text{ and }R_{2}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R_{2}.

$$4R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t^{2}}+12R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t}=qR_{2}$$

Reorder the terms.

$$4R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t^{2}}+12R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t}=R_{2}q$$

Combine all terms containing R_{1}.

$$\left(4\frac{\mathrm{d}(r)}{\mathrm{d}t^{2}}+12\frac{\mathrm{d}(r)}{\mathrm{d}t}\right)R_{1}=R_{2}q$$

The equation is in standard form.

$$0=R_{2}q$$

This is false for any R_{1}.

$$R_{1}\in$$

Solve for R_1

$$R_{1}\in \mathrm{R}$$

$$q=0\text{ and }R_{2}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R_{2}.

$$4R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t^{2}}+12R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t}=qR_{2}$$

Reorder the terms.

$$4R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t^{2}}+12R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t}=R_{2}q$$

Combine all terms containing R_{1}.

$$\left(4\frac{\mathrm{d}(r)}{\mathrm{d}t^{2}}+12\frac{\mathrm{d}(r)}{\mathrm{d}t}\right)R_{1}=R_{2}q$$

The equation is in standard form.

$$0=R_{2}q$$

This is false for any R_{1}.

$$R_{1}\in$$

Solve for R_2

$$R_{2}\neq 0$$

$$q=0\text{ and }R_{2}\neq 0$$

Steps for Solving Linear Equation

Variable R_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by R_{2}.

$$4R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t^{2}}+12R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t}=qR_{2}$$

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

$$qR_{2}=4R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t^{2}}+12R_{1}\frac{\mathrm{d}(r)}{\mathrm{d}t}$$

The equation is in standard form.

$$qR_{2}=0$$

Divide 0 by q.

$$R_{2}=0$$

Variable R_{2} cannot be equal to 0.

$$R_{2}\in \emptyset$$