Solve ∫ 1/5x+0.25y=5

$$\int \frac { 1 } { 5 } x + 0.25 y = 5$$

Solve for y

$$y=-4Сx-\frac{4x^{2}}{5}+20$$

Steps for Solving Linear Equation

Subtract \int \frac{1}{5}\mathrm{d}xx from both sides.

$$0.25y=5-\int \frac{1}{5}\mathrm{d}xx$$

Reorder the terms.

$$0.25y=-x\int \frac{1}{5}\mathrm{d}x+5$$

The equation is in standard form.

$$0.25y=-x\left(\frac{x}{5}+С\right)+5$$

Multiply both sides by 4.

$$\frac{0.25y}{0.25}=\frac{-x\left(\frac{x}{5}+С\right)+5}{0.25}$$

Dividing by 0.25 undoes the multiplication by 0.25.

$$y=\frac{-x\left(\frac{x}{5}+С\right)+5}{0.25}$$

Divide -x\left(\frac{x}{5}+С\right)+5 by 0.25 by multiplying -x\left(\frac{x}{5}+С\right)+5 by the reciprocal of 0.25.

$$y=-4x\left(\frac{x}{5}+С\right)+20$$

Solve for x

$$x=\frac{\sqrt{100+25С^{2}-5y}}{2}+С_{1}$$

$$x=-\frac{\sqrt{100+25С^{2}-5y}}{2}+С_{1}\text{, }y\leq 5С^{2}+20$$