Solve the differential equation

Evaluate

$$n^{\prime }=y$$

Rewrite the expression

$$\frac{dn}{dy}=y$$

Transform the expression

$$dn=ydy$$

$$\text{Integrate the left-hand side of the equation with respect to }n\text{ and the right-hand side of the equation with respect to }y$$

$$\int 1dn=\int ydy$$

Calculate

More Steps

Evaluate

$$\int 1dn$$

$$\text{Use the property of integral }\int kdx=kx$$

$$n$$

$$\text{Add the constant of integral }{C}_1$$

$$n+C_1,C_1\in \mathbb{R}$$

$$n+C_1=\int ydy,C_1\in \mathbb{R}$$

Calculate

More Steps

Evaluate

$$\int ydy$$

$$\text{Use the property of integral }\int x^{n}dx=\frac{x^{n+1}}{n+1}$$

$$\frac{y^{1+1}}{1+1}$$

Add the numbers

$$\frac{y^2}{1+1}$$

Add the numbers

$$\frac{y^2}{2}$$

$$\text{Add the constant of integral }{C}_2$$

$$\frac{y^2}{2}+C_2,C_2\in \mathbb{R}$$

$$n+C_1=\frac{y^2}{2}+C_2,C_1\in \mathbb{R},C_2\in \mathbb{R}$$

Solution

$$n=\frac{y^2}{2}+C,C\in \mathbb{R}$$

Show Solution