Solve f(D^2+4)y=pi

$$f ( D ^ { 2 } + 4 ) y = \pi$$

Solve for f (complex solution)

$$f=\frac{\pi }{y\left(D^{2}+4\right)}$$

$$D\neq -2i\text{ and }D\neq 2i\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by D^{2}+4.

$$\left(fD^{2}+4f\right)y=\pi$$

Use the distributive property to multiply fD^{2}+4f by y.

$$fD^{2}y+4fy=\pi$$

Combine all terms containing f.

$$\left(D^{2}y+4y\right)f=\pi$$

The equation is in standard form.

$$\left(yD^{2}+4y\right)f=\pi$$

Divide both sides by yD^{2}+4y.

$$\frac{\left(yD^{2}+4y\right)f}{yD^{2}+4y}=\frac{\pi }{yD^{2}+4y}$$

Dividing by yD^{2}+4y undoes the multiplication by yD^{2}+4y.

$$f=\frac{\pi }{yD^{2}+4y}$$

Divide \pi by yD^{2}+4y.

$$f=\frac{\pi }{y\left(D^{2}+4\right)}$$

Solve for f

$$f=\frac{\pi }{y\left(D^{2}+4\right)}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by D^{2}+4.

$$\left(fD^{2}+4f\right)y=\pi$$

Use the distributive property to multiply fD^{2}+4f by y.

$$fD^{2}y+4fy=\pi$$

Combine all terms containing f.

$$\left(D^{2}y+4y\right)f=\pi$$

The equation is in standard form.

$$\left(yD^{2}+4y\right)f=\pi$$

Divide both sides by yD^{2}+4y.

$$\frac{\left(yD^{2}+4y\right)f}{yD^{2}+4y}=\frac{\pi }{yD^{2}+4y}$$

Dividing by yD^{2}+4y undoes the multiplication by yD^{2}+4y.

$$f=\frac{\pi }{yD^{2}+4y}$$

Divide \pi by yD^{2}+4y.

$$f=\frac{\pi }{y\left(D^{2}+4\right)}$$

Solve for D (complex solution)

$$D=-\sqrt{\frac{\pi -4fy}{fy}}$$

$$D=\sqrt{\frac{\pi -4fy}{fy}}\text{, }y\neq 0\text{ and }f\neq 0$$

Solve for D

$$D=\sqrt{\frac{\pi -4fy}{fy}}$$

$$D=-\sqrt{\frac{\pi -4fy}{fy}}\text{, }\left(f\leq \frac{\pi }{4y}\text{ and }y>0\text{ and }f>0\right)\text{ or }\left(f\geq \frac{\pi }{4y}\text{ and }f<0\text{ and }y<0\right)\text{ or }\left(f=\frac{\pi }{4y}\text{ and }y<0\right)$$