Solve dx=3x^5/3/5+c

$$d x = \frac { 3 x ^ { 5 / 3 } } { 5 } + c$$

Solve for c

$$c=dx-\frac{3x^{\frac{5}{3}}}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5dx=3x^{\frac{5}{3}}+5c$$

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

$$3x^{\frac{5}{3}}+5c=5dx$$

Subtract 3x^{\frac{5}{3}} from both sides.

$$5c=5dx-3x^{\frac{5}{3}}$$

Divide both sides by 5.

$$\frac{5c}{5}=\frac{x\left(5d-3x^{\frac{2}{3}}\right)}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$c=\frac{x\left(5d-3x^{\frac{2}{3}}\right)}{5}$$

Divide x\left(5d-3x^{\frac{2}{3}}\right) by 5.

$$c=dx-\frac{3x^{\frac{5}{3}}}{5}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{3x^{\frac{2}{3}}}{5}+\frac{c}{x}\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&x=0\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5dx=3x^{\frac{5}{3}}+5c$$

The equation is in standard form.

$$5xd=3x^{\frac{5}{3}}+5c$$

Divide both sides by 5x.

$$\frac{5xd}{5x}=\frac{3x^{\frac{5}{3}}+5c}{5x}$$

Dividing by 5x undoes the multiplication by 5x.

$$d=\frac{3x^{\frac{5}{3}}+5c}{5x}$$

Divide 3x^{\frac{5}{3}}+5c by 5x.

$$d=\frac{3x^{\frac{2}{3}}}{5}+\frac{c}{x}$$