Solve f^prime(u)=5u^2+2n

$$f ^ { \prime } ( u ) = 5 u ^ { 2 } + 2 n$$

Solve for n

$$n=-\frac{5u^{2}}{2}$$

Steps for Solving Linear Equation

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

$$5u^{2}+2n=\frac{\mathrm{d}}{\mathrm{d}x}(f)u$$

Subtract 5u^{2} from both sides.

$$2n=\frac{\mathrm{d}}{\mathrm{d}x}(f)u-5u^{2}$$

The equation is in standard form.

$$2n=-5u^{2}$$

Divide both sides by 2.

$$\frac{2n}{2}=-\frac{5u^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$n=-\frac{5u^{2}}{2}$$

Solve for f (complex solution)

$$f\in \mathrm{C}$$

$$n=-\frac{5u^{2}}{2}$$

Solve for f

$$f\in \mathrm{R}$$

$$n=-\frac{5u^{2}}{2}$$