Solve ∫ x^2=4y-7x

$$\int x ^ { 2 } = 4 y - 7 x$$

Solve for y

$$y=\frac{x^{3}}{12}+\frac{7x}{4}+С$$

Steps for Solving Linear Equation

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

$$4y-7x=\int x^{2}\mathrm{d}x$$

Add 7x to both sides.

$$4y=\int x^{2}\mathrm{d}x+7x$$

The equation is in standard form.

$$4y=\frac{x^{3}}{3}+7x+С$$

Divide both sides by 4.

$$\frac{4y}{4}=\frac{\frac{x^{3}}{3}+7x+С}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$y=\frac{\frac{x^{3}}{3}+7x+С}{4}$$

Divide \frac{x^{3}}{3}+С+7x by 4.

$$y=\frac{x^{3}}{12}+\frac{С}{4}+\frac{7x}{4}$$

Solve for x

$$x=\sqrt[3]{\sqrt{36y^{2}+12Сy+С_{1}^{2}+343}+6y+С_{2}}+\sqrt[3]{-\sqrt{36y^{2}+12С_{3}y+С_{4}^{2}+343}+6y+С_{5}}$$