Solve dv=e^x^2dx

$$d v = e ^ { x ^ { 2 } } d x$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&v=xe^{x^{2}}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract e^{x^{2}}dx from both sides.

$$dv-e^{x^{2}}dx=0$$

Reorder the terms.

$$-dxe^{x^{2}}+dv=0$$

Combine all terms containing d.

$$\left(-xe^{x^{2}}+v\right)d=0$$

The equation is in standard form.

$$\left(v-xe^{x^{2}}\right)d=0$$

Divide 0 by v-e^{x^{2}}x.

$$d=0$$

Solve for v (complex solution)

$$\left\{\begin{matrix}\\v=xe^{x^{2}}\text{, }&\text{unconditionally}\\v\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$dv=dxe^{x^{2}}$$

Divide both sides by d.

$$\frac{dv}{d}=\frac{dxe^{x^{2}}}{d}$$

Dividing by d undoes the multiplication by d.

$$v=\frac{dxe^{x^{2}}}{d}$$

Divide e^{x^{2}}dx by d.

$$v=xe^{x^{2}}$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&v=xe^{x^{2}}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract e^{x^{2}}dx from both sides.

$$dv-e^{x^{2}}dx=0$$

Reorder the terms.

$$-dxe^{x^{2}}+dv=0$$

Combine all terms containing d.

$$\left(-xe^{x^{2}}+v\right)d=0$$

The equation is in standard form.

$$\left(v-xe^{x^{2}}\right)d=0$$

Divide 0 by v-e^{x^{2}}x.

$$d=0$$

Solve for v

$$\left\{\begin{matrix}\\v=xe^{x^{2}}\text{, }&\text{unconditionally}\\v\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$dv=dxe^{x^{2}}$$

Divide both sides by d.

$$\frac{dv}{d}=\frac{dxe^{x^{2}}}{d}$$

Dividing by d undoes the multiplication by d.

$$v=\frac{dxe^{x^{2}}}{d}$$

Divide e^{x^{2}}dx by d.

$$v=xe^{x^{2}}$$