Solve y=sin3x^2*dx

$$y = \sin 3 x ^ { 2 } \cdot d x$$

Solve for d

$$\left\{\begin{matrix}d=\frac{y}{\sin(3)x^{3}}\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$y=\sin(3)x^{3}d$$

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

$$\sin(3)x^{3}d=y$$

Divide both sides by \sin(3)x^{3}.

$$\frac{\sin(3)x^{3}d}{\sin(3)x^{3}}=\frac{y}{\sin(3)x^{3}}$$

Dividing by \sin(3)x^{3} undoes the multiplication by \sin(3)x^{3}.

$$d=\frac{y}{\sin(3)x^{3}}$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt[3]{\frac{y}{\sin(3)d}}\text{, }&d\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }d=0\end{matrix}\right.$$